Updated at 10:23 p.m. ET on 8/6
(CNN) – The decision to close a broad swath of American embassies and diplomatic posts across the Middle East in response to a terror threat was not an overreaction, President Barack Obama said Tuesday in his first remarks on the new security precautions.
The U.S. security posture throughout the Middle East, and especially in Yemen, was heightened after officials intercepted a message from al Qaeda leader Ayman al-Zawahiri to a top ally in Yemen telling him to "do something." A worldwide travel alert was issued, along with the slate of embassy and consulate closings.
The latest threat, Obama said, was a reminder that violent extremism still exists in the world. He stressed the importance of using caution and common sense while traveling abroad.
"The odds of dying in a terrorist attack are a lot lower than they are of dying in a car accident, unfortunately," Obama said.
The president spoke on NBC's "Tonight Show" with Jay Leno, which was taped in California and was to air later Tuesday evening. General notes about Obama's remarks were distributed by a pool of journalists traveling with the president.
Asked about Edward Snowden, who admitted to leaking details of U.S. classified surveillance programs, Obama said he was disappointed Russia had granted asylum to the former government contractor.
Russia's leaders, he said, have a proclivity for slipping into a Cold War mindset; though he added essential cooperation between the two nations continues.
The president will still attend September's Group of 20 summit in St. Petersburg, Russia, Obama said, though the White House has said an earlier meeting in Moscow between Russian President Vladimir Putin and Obama is under review.
Discussing Russia, Obama criticized a new law in the country barring public discussion of gay rights and relationships anywhere where children might hear it. The law has been condemned by Russian and international rights groups as highly discriminatory.
While Obama predicted Russia's treatment of gays and lesbians would not ultimately adversely affect its ability to host the 2014 Winter Olympics in Sochi, he did say he had little tolerance for nations who intimidate or harm citizens based on their sexual orientation.
Russia, he said, has a big stake in making next year's games successful – and a crackdown on gays and lesbians would prevent a successful Olympics.
On a pair of fellow politicians - and fellow 2008 candidates for president - Obama offered laughing assessments of Sen. John McCain, R-Arizona, and former Secretary of State Hillary Clinton.
The budding "bromance" between Obama and McCain - manifested Tuesday in the Republican senator's trip to Egypt at Obama's request - is akin to a romantic comedy, the president said.
"Initially, you're not getting along and then you keep bumping into each other," he joked.
In his opening monologue, Leno joked that McCain had been working with Egyptian leaders since "the King Tut administration."
And Clinton - enjoying a "post-administration glow" at their White House lunch last week - doesn't need to scope out the Oval Office ahead of an anticipated 2016 presidential bid. When Leno joked the former first lady may be measuring the drapes, Obama pointed out she has plenty of experience in the executive mansion.
"Keep in mind she's been there. She doesn't have to measure them," he said.