The International Association of Machinists and Aerospace Workers (IAM) union said 64% of its members voted against the proposed deal.
More than 30,000 of Boeing's employees have joined the walkout, which started on 13 September, after an initial offer was rejected.
Hours earlier Boeing's boss Kelly Ortberg warned that the company is at a "crossroads" as losses at the firm surged to roughly $6bn (£4.6bn).
“After 10 years of sacrifices, we still have ground to make up, and we're hopeful to do so by resuming negotiations promptly," union representatives said in a statement.
"This is workplace democracy – and also clear evidence that there are consequences when a company mistreats its workers year after year," it added.
Boeing has declined to comment on its latest offer being rejected.
Earlier, Mr Ortberg, who took over as chief executive in August, said he had been working "feverishly" to stabilise the firm, as it worked to repair its reputation, which has been hit by manufacturing and safety concerns.
"This is a big ship that will take some time to turn, but when it does, it has the capacity to be great again," he said.
The latest crisis at Boeing erupted in January with a dramatic mid-air blowout of a piece of one of its passenger planes.
Its space business also suffered a reputational hit after its Starliner vessel was forced to return to Earth without carrying astronauts.
The strike has compounded the problems, leading to a dramatic slowdown in production.
Mr Ortberg said the firm was "saddled with too much debt" and had disappointed customers with lapses in performance across the business.
Boeing's commercial aircraft business reported operating losses of $4bn in the last three months, while its defence unit lost nearly $2.4bn.
The strike "is costing them $100m a day so the cash burn is really significant... This is getting to a pretty severe situation for Boeing,” said Anna McDonald from Aubrey Capital Management.
Mr Ortberg argued the firm was in a strong position, with a backlog of roughly 5,400 orders for its planes.
But he warned investors that restar7ting the firm's factories, whenever the strike does end, will be tricky.
"It’s much harder to turn this on than it is to turn it off. So it’s critical, absolutely critical, that we do this right," he said.
"We have a detailed return-to-work plan in place and I’m really looking forward to getting everybody back and getting to work on that plan."
The company announced plans earlier this month to cut roughly 10% of its workforce. Thousands of other staff are already on a rolling furlough due to the strike, which has also hit suppliers.
Mr Ortberg told investors that his first priority was a "fundamental culture change".
"We need to prevent the festering of issues and work better together to identify, fix and understand root cause," he said. Boeing's suppliers are also feeling the impact of the strike.
Spirit AeroSystems, which makes plane bodies, has already announced a 21-day furlough for 700 of its workers.
It has also warned it could have to lay off staff if the Boeing strike continues beyond next month.Boeing says it aims to secure up to $35bn (£26.8bn) in new funding from investors and banks as a costly strike by thousands of its workers enters its second month.
Also on Tuesday, the union representing more than 30,000 of the aviation giant's workers held a rally in the city of Seattle.
The company is moving ahead with plans to lay off around 17,000 workers, with the first redundancy notices expected to be issued in mid-November.
Talks to end the walkout collapsed last week as the firm withdrew an offer that included a 30% pay rise over four years.
Boeing plans to raise up to $25bn in stock and debt offerings and said it had reached a deal with major banks to borrow as much much as $10bn.
"These are two prudent steps to support the company’s access to liquidity," Boeing said in a statement.
Major credit ratings agencies had previously warned that the strike could lead to downgrades, which would make it more expensive for the company to borrow money.
S&P Global estimated the strike is costing Boeing around $1bn a month.
The walkout, at a company of major importance to the US economy, has become a source of concern for the Biden administration.
On Monday, acting US Labor Secretary, Julie Su, met representatives of the International Association of Machinists and Aerospace Workers union (IAM) and Boeing executives in Seattle.
Meanwhile, top Washington state Congressional Democrats have called on Boeing and IAM to "redouble... efforts to reach a mutually beneficial resolution."
Israeli military forces besieged hospitals and shelters for displaced people in the northern Gaza Strip on Monday (Oct 21) as they stepped up their operations, preventing critical aid from reaching civilians, residents and medics said.
Troops rounded up men and ordered women to leave the Jabalia historic refugee camp, they said. An Israeli airstrike on a house in Jabalia killed five people and wounded several others, medics said.
The UN Palestinian refugee agency UNRWA said Israeli authorities were preventing humanitarian missions from reaching areas in the north of the Palestinian enclave with critical supplies, including medicine and food.
"People attempting to flee are getting killed, their bodies left on the street," UNRWA head Philippe Lazzarini said on X.
Medics at the Indonesian Hospital told Reuters that Israeli troops stormed a school and detained the men before setting it ablaze. The fire reached hospital generators and caused a power outage, they added.
Health officials said they had refused orders by the Israeli army, which started a new incursion into the territory's north over two weeks ago, to evacuate the three hospitals in the area or leave the patients unattended.
Later on Monday, Hussam Abu Safiya, director of Kamal Adwan Hospital said at least two critically wounded patients at the facility's intensive care unit died because of the lack of medical supplies.
"The hospital's blood units have run out completely... We are implementing a priority treatment method for patients. This is the reality," said Abu Safiya in a video message to media outlets.
Troops remained outside the hospital but did not enter, they said. Medics at a second hospital, Kamal Adwan, reported heavy Israeli fire near the hospital at night.
"The army is burning the schools next to the hospital, and no one can enter or leave the hospital," said one nurse at the Indonesian Hospital, who asked not to be named.
Palestinian health officials said at least 18 people had been killed in Jabalia and eight elsewhere in Gaza in Israeli strikes.
The Israeli military said in a statement its troops had dismantled infrastructure and tunnel shafts and killed alleged fighters in the Jabalia area.
Troops had helped thousands of civilians to evacuate safely through organised routes, it said, contradicting reports from the UN aid agency. Israel was in contact with the international community and Gaza's healthcare system to ensure hospital emergency services were operating, it said.
Last week, the United States told Israel it must take steps in the next month to improve the humanitarian situation in Gaza or face potential restrictions on US military aid.
Israel has intensified its campaigns both in Gaza and Lebanon after the killing of Hamas leader Yahya Sinwar last week had raised hopes of an opening for ceasefire talks to end more than a year of conflict.
It has vowed to eradicate Hamas, the group who formerly controlled Gaza and whose attack on Israel last year triggered the war, but in doing so has laid waste to much of the territory and killed tens of thousands of people. More than 1.9 million people have been left destitute and desperate for food.
"We are facing death by bombs, by thirst and hunger," said Raed, a resident of Jabalia camp. "Jabalia is being wiped out and there is no witness to the crime, the world is blinding its eyes."
Hadeel Obeid, a supervisor nurse at the Indonesian hospital, said they were running out of medical supplies, including sterile gauze and medications. The water supply has been cut off and there was no food for the fourth consecutive day, she told Reuters.
The United Nations said it had been unable to reach the three hospitals in northern Gaza.
The UN Human Rights Office accused Israeli forces of unlawful interference with humanitarian assistance and issuing orders that were causing forced displacement. It said their conduct "may be causing the destruction of the Palestinian population in Gaza's northernmost governate through death and displacement".
UNRWA'S Lazzarini said injured people were lying without care in hospitals that had been hit.
"UNRWA remaining shelters are so overcrowded, some displaced people are now forced to live in the toilets," he said.
Israel says it is getting large quantities of humanitarian supplies into Gaza with land deliveries and airdrops. It also says it has facilitated the evacuation of patients from the Kamal Adwan Hospital.
Palestinians say no aid entered northern Gaza areas where the operation is active.
Reuters reported earlier this month that food supplies have fallen sharply since Israeli authorities introduced a new customs rule on some humanitarian aid and are separately scaling down deliveries organised by businesses.
Israeli soldiers look on from atop a military vehicle near the Israel-Gaza border, amid the ongoing conflict in Gaza between Israel and Hamas, in southern Israel, Oct 21, 2024.
Residents and medics said Israeli forces had tightened their siege on Jabalia by positioning tanks in nearby Beit Hanoun and Beit Lahiya towns and ordering residents to leave.
Israeli officials said evacuation orders were aimed at separating Hamas fighters from civilians and denied there was any systematic plan to clear out civilians. It said its forces operating in northern Gaza killed scores of people it accused of being Hamas gunmen.
Hamas accused Israel of carrying out acts of "genocide and ethnic cleansing" to force people to leave northern Gaza. Israel also faces charges of violations of the 1948 Genocide Convention at the International Court of Justice.
The Hamas armed wing said fighters attacked forces there with anti-tank rockets and mortar fire, and detonated bombs against troops inside tanks and stationed in houses.
Elsewhere in the enclave, Israeli strikes killed at least five people in Rafah in the southern Gaza Strip and four in two separate strikes in Gaza City, medics said.
The slain Sinwar was one of the alleged masterminds of the Oct 7, 2023, cross-border attack on Israeli communities that killed around 1,200 people, with about 253 more taken back to Gaza as hostages, according to Israeli tallies.
Israel's subsequent bombardment of Gaza has killed more than 42,500 Palestinians, with another 10,000 uncounted dead thought to lie under the rubble, Gaza health authorities say.
