He was replying to a CNN interviewer who called India's leader an "illiberal democrat" and asked how President Biden should engage with such people
Mr Obama's remarks, made in an interview with CNN's Christiane Amanpour which was aired before the Congress address, were widely reported in India.
Ms Amanpour referred to the "threat to democracy" from so-called "illiberal democrats" before referring to Mr Modi as one.
"How should a president engage with those kinds of leaders, either in the naming of them or in the dealing with them?" she asked.
Mr Obama said it was "complicated", before referring to his own experience dealing with allies who may not have run "ideally democratic governments" but with whom relations had to be maintained for a number of reasons. He added that it was "appropriate" for the US president, when possible, to challenge "trends that are troubling" either in public or private.
"If the president meets with Prime Minister Modi, then the protection of the Muslim minority in a majority Hindu India - that's something worth mentioning. If I had a conversation with Prime Minister Modi, who I know well, part of my argument would be that if you do not protect the rights of ethnic minorities in India, then there is a strong possibility that India at some point starts pulling apart," he said, adding that that would be contrary to India's interests.
Prominent ministers from India’s ruling party have derided comments by former US President Barack Obama that Prime Minister Narendra Modi’s government should protect the rights of minority Muslims, accusing him of being hypocritical.
During Modi’s state visit to the United States last week, Obama told CNN the issue of the “protection of the Muslim minority in a majority-Hindu India” would be worth raising in his meeting with US President Joe Biden.
Obama said without such protection there was “a strong possibility that India at some point starts pulling apart”.
Indian Defence Minister Rajnath Singh on Monday said Obama “should not forget that India is the only country which considers all the people living in the world as family members”.
“He should also think about himself as to how many Muslim countries he has attacked,” added Singh, whose statement came a day after another top Indian minister slammed the former US president for his remarks.
Finance Minister Nirmala Sitharaman on Sunday said she was shocked that Obama made such remarks when Modi was visiting the US aiming to deepen relations.
“He was commenting on Indian Muslims … having bombed Muslim-majority countries from Syria to Yemen … during his presidency,” Sitharaman told a press conference on Sunday.
“Why would anyone listen to any allegations from such people?”
The US Department of State has raised concerns over the treatment of Muslims and other religious minorities in India under Modi’s Hindu nationalist party. The Indian government says it treats all citizens equally.
Biden said he discussed human rights and other democratic values with Modi during their talks at the White House.
