Obama also said Trump's suggestion he might not back NATO allies show he's unprepared to handle foreign policy, in an interview aired Sunday.
Obama's comments came in an interview with CBS' John Dickerson on "Face the Nation." The day before the Democratic National Convention's kickoff, the President made clear he's eager to attack Trump over foreign policy.
He lambasted Trump for suggesting the United States should refuse to assist NATO allies who haven't contributed enough financially to the trans-Atlantic alliance.
"I think that anybody who's been paying attention knows there is a big difference between challenging our European allies to keep up their defense spending, particularly at a time when Russia's been more aggressive, and saying to them, 'You know what? We might not abide by the central tenant of the most important alliance in the history of the world,'" Obama said.
He added: "One that was built by Democrats and Republicans and has been a cornerstone of U.S. foreign policy since the end of World War II. And, you know, for Mr. Trump, who has in the past suggested that America's weak and not looking out for its allies, to then maybe not have enough information or understanding to go out and say that America might not stand by its solemn commitment to protect those same allies who stood with us after 9/11 when we were attacked, I think is an indication of the lack of preparedness that he has been displaying when it comes to foreign policy."
Obama also criticized Trump over his proposed restrictions on Muslims' travel.
He said the Muslim-American community in the United States "feels deeply American and deeply committed to upholding the rule of law, and working with law enforcement, and rejecting intolerance and extremism that's represented by the perversions of Islam that ISIL is sending out through the internet or carrying out in the Middle East."
"But that requires leaders, political leaders, religious leaders, business leaders, all of us to send a very clear signal that we are not going to be divided in that fashion," Obama said. "And I think the kinds of rhetoric that we've heard too often, from Mr. Trump and others, is ultimately helping do ISIL's work for us."