In his first comments on the latest security threat from Al Qaeda since the State Department urged Americans to leave Yemen, President Obama said the threat of an imminent terrorist attack against Americans is "significant enough that we're taking every precaution."

Speaking on NBC's "Tonight Show," broadcast Tuesday evening, Obama told host Jay Leno that Americans should go ahead with summer travel plans abroad despite global travel warnings. But he said they should "show some common sense" and recognize that some countries are more dangerous than others.

He didn't specify which countries posed the greatest threat. He also wouldn't say whether the U.S. learned of the threat through National Security Agency Surveillance programs. Nineteen U.S. embassies and consulates in 16 countries have been ordered closed to the public until Saturday. 

Obama also made his first comments about National Security Agency leaker Edward Snowden, saying that he was "disappointed" that Russia granted him temporary asylum.

"There have been times where they slip back into Cold War thinking and a Cold War mentality," Obama said.

Snowden, an ex-NSA systems analyst, is accused of leaking details about highly-secretive government surveillance programs. He spent several weeks in the transit zone of a Moscow airport before being granted asylum for a year.

Obama also lauded two of his former political rivals: former Secretary of State Hillary Rodham Clinton and Sen. John McCain, R-Ariz.

When Leno brought up a White House lunch that Clinton and Obama shared last week, Obama acknowledged that he had invited the former Secretary of State, saying Clinton "had that post-administration glow ... when folks leave the White House like two weeks later, they look great."

The president also discussed the status of Obamacare, and maintained that previously uninsured Americans would be eligible to sign up to receive health insurance on October 1.