President Barack Obama hit back hard in a "60 Minutes" interview broadcast Sunday at Mitt Romney's criticisms of his handling of Syria and Iran, saying that if the Republican standard-bearer "is suggesting that we should start another war, he should say so."

Obama also brushed aside talk that Israeli Prime Minister Benjamin Netanyahu has been pressuring him to take a harder line on Iran's suspicious nuclear program — source of some of Romney's sharpest campaign-trail criticisms.

"When it comes to our national security decisions-- any pressure that I feel is simply to do what's right for the American people. And I am going to block out any noise that's out there," the president said.

"Now I feel an obligation -- not pressure but obligation -- to make sure that we're in close consultation with the Israelis-- on these issues, because it affects them deeply," Obama said. "They're one of our closest allies in the region. And we've got an Iranian regime that has said horrible things that directly threaten Israel's existence."

Romney has accused Obama of not doing enough to curb Iran's nuclear program, which Tehran says is a civilian energy program but America and its allies say is an effort to develop the ability to build a nuclear weapon. He has also charged that the president has done too little to help rebels against Syrian strongman Bashar al-Assad topple his regime as the civil war there has left perhaps as many as 20,000 dead.

Asked about those criticisms, Obama bristled.

"Let's see what I've done since I came into office: I said I'd end the war in Iraq. I did. I said that we'd go after Al Qaeda. They've been decimated in the FATA," he said, referring to Pakistan's Federally Administered Tribal Areas, along the remote border with Afghanistan. "That we'd go after Bin Laden. He's gone. So I've executed on my foreign policy. And it's one that the American people largely agree with."

"So if Governor Romney is suggesting that we should start another war, he should say so," Obama said. That remark echoed suggestions from some of the president's advisers that Romney relies on so-called "neoconservative" advisers like those who championed the war in Iraq under President George W. Bush.

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The interview — and a companion question-and-answer session with Romney — ran as Obama was poised to head to New York on Monday for the annual U.N. General Assembly, a brief pirouette on the world stage before he heads back out on the campaign trail. He will address the U.N. on Tuesday — exactly six weeks before Election Day — and then head out to the pivotal battleground of Ohio a day later.

The president won't hold separate meetings with any key world leaders, citing scheduling concerns. But Obama and First Lady Michelle Obama have found time to sit down Monday with the ladies of "The View" to tape an interview.

(White House aides did not rule out that the president could have "pull-aside" discussions with world leaders. It's just what it sounds like: The president pull aside another head of state or government on the margins of a U.N. meeting for a quick chat.)

Last year, Obama used his general assembly speech to rebuke the Palestinians for trying to get the world body to essentially grant the status of a state. This year, the president is expected to blend a full-throated defense of his handling of foreign policy with a new warning to Iran. And he is expected to address the violent turmoil in the Middle East, notably in countries that saw the so-called "Arab Spring" uprisings sweep away longstanding authoritarian regimes.

"There are going to be bumps in the road," he said "There are strains of extremism, and anti-Americanism, and anti-Western sentiments." "There will probably be some times where we bump up against some of these countries and have strong disagreements, but I do think that over the long term we are more likely to get a Middle East and North Africa that is more peaceful, more prosperous and more aligned with our interests," he said. (After the interview, both the Romney campaign and the Republican National Committee mocked Obama's use of "bumps in the road" in connection to the unrest).

Obama tends to get higher marks from the American public on foreign policy than on other issues — notably, the economy, which is the dominant issue on voters' minds. But he has seen his advantage over Romney shrink somewhat.

For his part, Romney has struggled to level more than rhetorical criticisms of Obama's foreign policy — sometimes sounding like he'd rather take on the Obama of 2008, who pledged to hold talks with leaders of Iran without preconditions, than the Obama of 2012, who has sharply escalated economic sanctions on the Islamic republic and reportedly unleashed unprecedented cyberwarfare to derail its nuclear program.

Still, the incumbent faces a dismaying number of foreign policy problems.

Bombings regularly rock Iraq, where the war isn't over — America is just not as involved. And it seems like each week brings a new report of Afghan security forces killing their NATO and American counterparts. Iran defies international pressure to halt its suspect nuclear program, while civil war rages in Syria. Russia has moved to expel American aid workers. Violent protests have struck U.S. diplomatic posts in the Muslim world, and extremists who have yet to be formally identified stormed the consulate in Benghazi and killed the American ambassador — marking the anniversary of 9-11 with a terrorist attack. China's territorial disputes with some of its neighbors have escalated.