In accepting his party’s renomination a week ago, President Obama called himself a “tested and proven” leader in a dangerous world of threats from abroad, especially from the terrorist-spawning Middle East.

“The historic change sweeping across the Arab world must be defined not by the iron fist of a dictator or the hate of extremists, but by the hopes and aspirations of ordinary people who are reaching for the same rights that we celebrate here,” Mr. Obama said at the Democratic National Convention, poking fun at Republican rival Mitt Romney for saber-rattling and for being “new” to foreign policy.

But a week later, with Muslim protests flaring at U.S. diplomatic posts across the Middle East and with four Americans killed in Libya, the gentler foreign policy pillar upon which Mr. Obama supports his re-election bid is in danger of toppling. As images of Muslims chanting “Death to America” evoke memories of the Iranian hostage crisis in 1979, critics are calling Mr. Obama weak.

Sen. John McCain, the Arizona Republican who lost the 2008 election to Mr. Obama, criticized the president Thursday for “feckless foreign policy” that he said is harming relations with the Middle East.

“What this is all about is American weakness and the president’s inability to lead,” Mr. McCain said on NBC’s “Today” show.

A Middle East analyst at the Council on Foreign Relations in New York, Isobel Coleman, acknowledged the domestic political peril for Mr. Obama in the burgeoning crisis.

“You’ve had, for the first time since 1979, a U.S. ambassador killed, and it demands … much more serious attention, I think, from the president,” she told reporters. “Of course, it’s also become an election issue, with the Romney campaign saying … that Obama wasn’t clear and forceful enough.”

Former Defense Secretary Donald H. Rumsfeld said on his Twitter account, “The Attacks On Our Embassies & Diplomats Are A Result Of Perceived American Weakness. Mitt Romney Is Right To Point That Out.”

The president said the killings of U.S. Ambassador J. Christopher Stevens and three other Americans will not deter his current course in the Middle East.

“I want people around the world to hear me, to all those who would do us harm, no act of terror will go unpunished,” Mr. Obama said Thursday at a campaign rally in Golden, Colo. “It will not dim the light of the values that we proudly present to the rest of the world. No act of violence shakes the resolve of the United States of America.”

Up until now, Mr. Obama has enjoyed a clear advantage over Mr. Romney on foreign policy in polls. A Wall Street Journal/NBC News survey last month found that 54 percent of respondents approved of the president’s handling of foreign policy, while 40 percent disapproved. Asked who would be a better commander in chief, 45 percent said Mr. Obama and 38 percent said Mr. Romney.

In 2009, after nearly eight years of war under President George W. Bush in the post-9/11 era, Mr. Obama promised a new beginning with the Arab world in a celebrated speech in Cairo. But James Carafano, a defense and foreign policy analyst at the conservative Heritage Foundation, said Mr. Obama’s approach to the Middle East since then has been “an abject failure.”

“I can’t say right now U.S. policies contribute to the violence, but, given the state of U.S. policy, what does it matter?” Mr. Carafano said in an interview. “The notion that the Cairo speech and soft-peddling the war on terror was going to solve America’s image problem was a weird admixture of naivety and hubris. In running away from Iraq and Afghanistan, downsizing the military, and saying we need austerity in the military and a pivot to Asia, U.S. policy just feeds the al Qaeda narrative that the U.S. is a paper tiger and can be pushed away if prodded.”

Mr. Carafano said the Obama administration has wasted valuable time negotiating over Iran’s nuclearization and Syria’s bloody crackdown on pro-democracy rebels.

“The White House response to the Arab Spring has been reactive from the get-go, doing what it has to do to get the White House out of the headlines and then just trying to put policy back on cruise control,” Mr. Carafano said. “The counterterrorism policy is an abject failure, because it has focused myopically on whacking al Qaeda leaders and not dealing the extremist movement as the global insurgency that it is; so the network is weaker, but the movement is spreading. Instead of one big Afghanistan, we are going to have lots of little ones. It should come as no surprise that extremists would use these tactics to exploit the U.S. gaps in the U.S. strategy.”

Denis McDonough, a deputy national security adviser to Mr. Obama, defended the administration’s approach this week in a speech to the U.S. Conference of Catholic Bishops in Washington, saying it’s a policy based on American values.

“In Egypt, Libya, Syria and all of the Arab Spring countries in transition, the United States will continue to stand for a set of principles that history shows leads to progress and opportunity,” Mr. McDonough said. “That includes the protection of universal rights, including the freedom of religion. For these transitions to succeed, and for these countries to achieve their full potential, all faiths must be respected and protected.”

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