WASHINGTON — President Barack Obama, defending his foreign policy record at a time of anti-American rage in the Muslim world, fired back at suggestions from Republican Mitt Romney that the president has been weak with allies and enemies alike.

In an interview airing the night before Obama meets with world leaders at the United Nations, the president said, “If Gov. Romney is suggesting that we should start another war, he should say so.”

It was Obama’s most direct rebuttal yet to persistent skepticism by his White House rival on his handling of an unraveling situation in the Middle East. Romney has charged the U.S. stance has been marred by miscalculations, mixed messages and appeasement.

As far back as May, Romney was condemning Obama’s response to unrest in Syria, dubbing it a “policy of paralysis” and calling for more assertive measures, such as arming the opposition to Syrian President Bashar Assad. As deadly anti-American protests erupted earlier this month in Libya and elsewhere, Romney sought to undercut what polling shows is a significant foreign policy edge for Obama by calling the president’s handling of the situation “disgraceful” and decrying a lack of U.S. leadership in the region.

In a companion interview to Obama’s appearance on CBS’ “60 Minutes,” Romney broadened his reproach to include Israel, criticizing Obama’s failure to meet with the U.S. ally’s head of state, Benjamin Netanyahu, during the annual U.N. gathering. Romney called it a mistake that “sends a message throughout the Middle East that somehow we distance ourselves from our friends.”

The White House has said scheduling precluded a meeting between the two leaders, who won’t be in New York at the same time. With the final six weeks of a hard-fought election hanging over the U.N. summit, Obama has opted out of face-to-face meetings with any of his counterparts — not just Netanyahu — during his compressed U.N. visit.

But Obama pushed back on the notion that he feels pressure from Netanyahu, who has called for the U.S. to lay out a “red line” that Iran’s nuclear program mustn’t cross to avoid American military intervention.

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

In a wide-ranging interview conducted the day after U.S. Ambassador to Libya Chris Stevens was killed in an attack on Benghazi, Obama defended his foreign policy successes, noting he’d followed through on a commitment to end the war in Iraq and had nabbed al-Qaida leader Osama bin Laden.

He also waxed optimistic that winning a second term would give him a mandate to overcome obstructionism from congressional Republicans whose No. 1 goal, he said, has been to prevent his re-election.

Romney, in an interview conducted last week, sought to deflect attention from his running mate, Wisconsin Rep. Paul Ryan, over their differences in Medicare policy: “I’m the guy running for president, not him.”

While reaffirming his commitment to lowering all income tax rates by 20 percent, Romney expressed no unease about his refusal to offer specifics, such as which loopholes and deductions he’d eliminate to pay for the cuts.

“The devil’s in the details. The angel is in the policy, which is creating more jobs,” Romney said, adding that he doesn’t want to see overall government revenue reduced.

Addressing the seemingly unshakable charge of flip-flopping on policy issues, Romney pointed the finger at Obama, noting his changes of heart on gay marriage and military tribunals for terrorism suspects.

“Have I found some things I thought would be effective turned out not to be effective? Absolutely,” Romney said. “You don’t learn from experience, you don’t learn from your mistakes —why, you know, you ought to be fired.”

The series of interviews also offered glimpses into both candidates’ personal habits, including their late-night routines. Romney said his nightly prayer is a time to connect both with the divine and with his own thoughts, and said he asks God mainly for wisdom and understanding.

Obama, describing himself as “a night guy,” said that after first lady Michelle Obama and their daughters retire around 10 p.m., he hunkers down for reading, writing and occasionally a moment alone on the Truman Balcony, with the Washington Monument and Jefferson Memorial in view.

“Those are moments of reflection that, you know, help gird you for the next challenge and the next day,” Obama said.

The “60 Minutes” interviews came as Romney’s campaign strove to turn the page on a week of public stumbles and Republican hand-wringing, promising a redoubled effort in the most competitive states to undercut Obama’s economic record as voters tune in for the final six weeks of a deadlocked race.

A secretly recorded video released last Monday showed Romney writing off his prospects for winning over the almost half of Americans who he said pay no taxes, are dependent upon government and see themselves as victims dominated the week. Ahead of an evening campaign stop at a Denver-area high school Sunday, Romney huddled with senior advisers in Los Angeles to rehearse for the three upcoming presidential debates, which his aides see as the best opportunity to get his campaign and its message back on track.

Amid mounting pressure to spend less time raising money and more time explaining his plans to voters, Romney was refocusing his schedule on the most competitive states. “We’re going to keep on campaigning hard,” he told reporters Sunday. “I think the fundraising season is probably a little quieter going forward.”

Romney blamed Obama’s decision to bypass traditional spending limits during the 2008 campaign. “I’d far rather be spending my time out in the key swing states campaigning door to door if necessary, but in rallies and various meetings,” he said. “But fundraising is part of politics when your opponent decides not to live by the federal spending limits.”

After Colorado, Romney was to begin a three-day bus tour in Ohio on Monday followed by a stop in Virginia — states that Obama won in 2008 but that Republicans claimed four years earlier.

While national polls remain tight, polls in several of the most closely watched states, including Colorado, suggest Obama has opened narrow leads. Obama won Colorado by 9 points four years ago, but the state went to a Republican in the previous three presidential elections.

Asked Sunday about the poll numbers, Romney replied, “I know that in the coming six weeks they’re very unlikely to stay where they are today.”

Obama took a rare weekend break from the campaigning ahead of his U.N. address Tuesday, but dispatched top allies to the Sunday talk shows to try to keep Romney’s missteps alive in the minds of a dwindling cadre of undecided voters.