WASHINGTON — President Obama drew praise from unlikely quarters on Monday for pursuing a risky and clandestine mission to kill Osama bin Laden, a successful operation that interrupted the withering Republican criticism about his foreign policy, world view and his grasp of the office.

Former Vice President Dick Cheney declared, “The administration clearly deserves credit for the success of the operation.” New York’s former mayor, Rudolph W. Giuliani, said, “I admire the courage of the president.” And Donald J. Trump declared, “I want to personally congratulate President Obama.”

As fleeting as it might prove to be, the positive tone stood in blunt contrast to the narrative Republicans have been working to build in the opening stages of the 2012 presidential campaign.

The argument that most potential Republican candidates have been making — that Mr. Obama is an indecisive leader, incapable of handling rapidly evolving events around the world — suddenly became more complicated. And the boost in stature for Mr. Obama, even if temporary, comes when a number of Republicans are deciding whether to commit themselves to the presidential race, and offered fresh evidence that he might be less vulnerable than his opponents thought.