Trump "doesn't appear to have basic knowledge around critical issues" in Europe, the Middle East or Asia, and he's shown himself to be "woefully unprepared to do this job," Obama said in response to a question at a White House news conference with Singapore Prime Minister Lee Hsien Loong, Bloomberg wrote.

Obama questioned how top Republicans, including House Speaker Paul Ryan, Senate Majority Leader Mitch McConnell and veteran lawmakers like Senator John McCain, can regularly denounce Trump's statements while still supporting his bid for the presidency.

Read alsoNYT: How Paul Manafort wielded power in Ukraine before advising Donald Trump"The question I think they have to ask themselves is, if you are repeatedly having to say in very strong terms that what he has said is unacceptable, why are you still endorsing him?" Obama said. "What does this say about your party that this is your standard bearer? This isn't a situation where you have an episodic gaffe. This is daily. Weekly."

Trump has become embroiled in numerous controversies through his campaign, including suggesting former POW McCain wasn't a hero, saying a federal judge was biased because of his Mexican ancestry, and, more recently, disparaging a Muslim couple, Khizr and Ghazala Khan, whose son was an Army captain killed in Iraq in 2004, after they criticized his proposed ban on Muslims entering the country at the Democratic convention last week.

In additional remarks at a news conference and in interviews last week, Trump also appeared to be confused or ignorant of Russia's military operations in Ukraine since 2014; asked the Russian government to hack into Democratic nominee Hillary Clinton's e-mails – he later said he was being sarcastic – and criticized four-star Marine Corps General John Allen after he also denounced Trump's policies at the Democratic convention.