WASHINGTON — Mitt Romney’s repeated denunciation of President Obama in the aftermath of the deadly assault on the U.S. consulate in Benghazi, Libya, is a high-risk political calculation that could damage a campaign that has been declining in the polls since the end of the Republican National Convention, political analysts said Wednesday.

Romney sparked the controversy shortly after news of the North African attacks broke Tuesday night when he declared, “It’s disgraceful that the Obama administration’s first response was not to condemn attacks on our diplomatic missions, but to sympathize with those who waged the attacks.”

The Republican nominee reinforced his critique Wednesday, telling reporters in Florida that a statement released by the U.S. embassy in Egypt, which denounced religious hatred of any kind, was “akin to apology” and that it was “disgraceful to apologize for American values.”

Romney’s response to the violence that killed four Americans in North Africa was criticized by strategists from both parties.

“Mitt Romney’s words were a terrible mistake,” said Cindy Rugeley, a political science professor at Texas Tech University. “Criticizing a president at a time of national tragedy is never a good idea.”

Rep. Peter T. King, R-N.Y., chairman of the House Homeland Security Committee, told reporters on Capitol Hill, “I probably would have waited 12 or 24 hours and put out a more comprehensive statement.” Romney’s statement “can be perceived as being political.”

Republicans, remembering 2008 nominee John McCain’s mid-September meltdown amid the cascading financial crisis on Wall Street, are hoping that the North Africa story will quickly fade away — but they fear the worst.

“This could be a game-changer,” Alex Castellanos, a 2008 Romney campaign adviser who is not employed by the campaign this year, said on CNN.

Peggy Noonan, a conservative commentator, former speechwriter for Presidents Ronald Reagan and George H.W. Bush, told Fox News: “When you step forward in the midst of a political environment and start giving statements on something dramatic and violent that has happened, you’re always leaving yourself open to accusations that you are trying to exploit things politically. Sometimes when really bad things happen, when hot things happen, cool words or no words is the way to go.”

Romney’s harsh tone stood in contrast to the response of House Speaker John Boehner, R-Ohio, and Senate Democratic Leader Harry Reid, D-Nev., who appeared together and called on the nation to come together in a time of adversity.

The Romney remarks, which brought a rebuke from Obama late Wednesday afternoon, came after a week of declining poll numbers for the Republican presidential nominee. Six national polls taken in the past week show the Democratic incumbent in the lead after the race was a dead heat for the previous month. The discussion of the North African attacks also shifted the Romney campaign’s focus from the economy to international affairs, much to the glee of Democrats. A recent CNN/ORC International poll found that American voters, by 54 percent to 42 percent, believe that Obama is better prepared than Romney to handle foreign policy issues. Obama weighed in Wednesday afternoon, chiding Romney in an interview with CBS News’ Steve Kroft.

“There’s a broader lesson to be learned here: Gov. Romney seems to have a tendency to shoot first and aim later,” Obama said. “And as president, one of the things I’ve learned is you can’t do that. It’s important for you to make sure that the statements that you make are backed up by the facts and that you’ve thought through the ramifications before you make them.”