NEW YORK >> Republican Mitt Romney on Tuesday accused President Barack Obama of politicizing the death of Osama bin Laden a year ago but said it was "totally appropriate" for him to claim credit for ordering the U.S. military raid that ended with the terrorist leader’s death in a hideout in Pakistan.

Obama’s re-election campaign has used his decision to suggest that Romney would not have made the same call. Romney, the president’s all-but-certain Republican challenger in the fall election, says he would have.

Marking the anniversary at a New York City fire house that lost 11 men on Sept. 11, 2001, Romney said he understood the president’s desire to take credit for killing one of the world’s most-wanted men.

"It’s totally appropriate for the president to express to the American people the view that he has that he had an important role in taking out Osama bin Laden," Romney said after visiting the lower Manhattan fire station with Rudy Giuliani, who was mayor when terrorists flew planes into the World Trade Center’s twin towers and killed nearly 3,000 people.

"I think politicizing it and trying to draw a distinction between himself and myself was an inappropriate use of the very important event that brought America together," Romney said.

He and Giuliani had just eaten pizza with several fire fighters.

For his part, Obama marked the occasion by putting the power of incumbency on display. He flew unannounced to Afghanistan to sign an agreement cementing the U.S. commitment to that country after the war there ends. His predecessor, Republican George W. Bush, sent troops there shortly after 9/11 to eradicate Taliban and al-Qaida forces.

Romney insisted that he would have ordered the strike on bin Laden’s hideout in Pakistan.

"This is a person who had done terrible harm to America and who represented a continuing threat to civilized people throughout the world," Romney said, echoing his comments from a day earlier. "Had I been president of the United States I would have made the same decision."

Democrats have pointed to Romney’s suggestion when he ran for president in 2008 that he would have taken a different course of action. He said in 2007 that it was "not worth moving heaven and earth" to catch one person.

Asked about the matter at the White House on Monday, Obama suggested — without saying Romney’s name — that people should be held accountable for past statements about the pursuit of bin Laden.

Giuliani, a former Romney rival and critic who since has endorsed the former Massachusetts governor’s bid, also said Obama shouldn’t use the anniversary to attack Romney.

"If he wants to take credit for it I have no problem with that at all. I wish he wouldn’t use it as a source of negative campaigning. I think that’s a big mistake," he said.

Romney also tried to clarify another comment from 2007, when candidate Obama was being criticized for saying he would conduct unannounced raids inside Pakistan if high-level terror targets were found to be hiding there. Romney criticized Obama at the time, saying: "I do not concur in the words of Barack Obama in a plan to enter an ally of ours."

Romney suggested Tuesday that he had simply criticized Obama for signaling his intentions about what he would do as president.

"We always reserve the right to go anywhere to get Osama bin Laden," Romney said. "I said that very clearly in the response that I made, but that I thought — and many people believed as I did — that it was naive on the part of the president at that time, the candidate, to say he would go into Pakistan."

Before visiting the fire station, Romney ate breakfast with the current mayor, Michael Bloomberg, a Republican-turned-independent who has avoided endorsing anyone in the presidential race so far.

Asked whether he would make an endorsement, Bloomberg didn’t shut the door.

"I’ll see down the road," he said after Romney had departed. He said Obama and Romney are "both very smart, very formidable candidates. They’re very different and they give the public a real choice."