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For a late-night comic Jay Leno certainly covered some serious ground with President Obama on Tuesday evening.

Mr. Obama, making his 6th appearance on NBC’s “Tonight Show,” and his fourth as president, told his host that the government is not overreacting in locking down nearly 20 diplomatic posts and issuing a worldwide travel warning after intercepted electronic conversations raised concerns of terrorist attacks abroad.

Americans should proceed with vacations in a “prudent way, “ Mr. Obama said during the taped appearance, and check the State Department Web site for updates. “The odds of dying in a terrorist attack,” he added, “are a lot lower than they are of dying in a car accident, unfortunately.”

While the White House has declined to use the latest reports of terrorist threats to justify the administration’s broad intelligence surveillance programs in the United States and in foreign countries, Mr. Obama did reiterate that such government surveillance is a “critical component to counterterrorism.” In both parties in Congress, however, lawmakers are trying to limit the intelligence-gathering.

The president stated flatly that he would attend the G-20 summit of the world’s wealthiest countries and developing nations in St. Petersburg, Russia, next month. His attendance was in question after Russia granted temporary asylum to Edward J. Snowden, the former intelligence contractor who disclosed the surveillance programs of the National Security Agency, igniting a global controversy. Still up in the air, however, is whether Mr. Obama will scrap plans to meet Mr. Putin in Moscow separately.

Mr. Obama seemed to dismiss Russia’s action as the predictable blip in an otherwise constructive relationship. “There are times when they slip back into Cold War thinking and Cold War mentality,” he said. “What I continually say to them and to President Putin — that’s the past.”

The president also said he did not think a controversy over Russia’s anti-gay policies would disrupt next year’s Winter Olympics in that country, despite calls from some gay-rights activists for international boycotts.

On domestic politics, Mr. Obama, still in the same dark suit and blue tie he had worn hours earlier in a steamy Phoenix high school gym for a speech on housing policies, repeated some of his talking points on that subject. And he commiserated with Mr. Leno about the inability to get bipartisan agreement in Congress on initiatives like federal assistance for public works projects and road repairs.

Mr. Obama’s press secretary, Jay Carney, when he was asked earlier in the day why Mr. Obama so often resorts to such unorthodox media outlets, said, “We’re trying to communicate with Americans where they are. And the viewers of late-night shows are not necessarily the readers of newspapers or wire services, or necessarily viewers of cable or broadcast news shows.”

“Some of his more substantive interviews have appeared in non-traditional settings,” Mr. Carney added. “So you never know what you might get.”

One of the lightest moments came when Mr. Leno questioned Mr. Obama about his budding “bromance” with his bitter 2008 Republican rival, Senator John McCain of Arizona.

“That’s how a classic romantic comedy goes,” Mr. Obama quipped. “Initially you’re not getting along and then you keep bumping into each other.”

As for his other 2008 rival-turned-ally, former Secretary of State Hillary Rodham Clinton, Mr. Obama said that she arrived for their recent lunch in the White House with “that post-administration glow.” He and Mrs. Clinton were “genuinely close,” he said.

When Mr. Leno asked if Mrs. Clinton was measuring for drapes at the White House, Mr. Obama was quick to reply, “Keep in mind she’s been there. She doesn’t have to measure them.”

Mr. Leno had begun the show by wishing Mr. Obama a happy birthday – the president turned 52 on Sunday – but it was Mr. Leno who got a present at the end of the taping. Mr. Obama gave Mr. Leno, a car enthusiast, a toy model of the presidential limousine known as “The Beast.”

“Oh, cool!” Mr. Leno said and repeated, predictably enthused.