Former vice president Richard B. Cheney has been a harsh critic of the Obama administration’s actions against terrorism, accusing the White House last year of being “slow” to “come to the recognition that we are at war.”

On Monday, Cheney struck a decidedly different tone.

“I also want to congratulate President Obama and the members of his national security team,” Cheney said, after commending military and intelligence professionals for the killing of Osama bin Laden.

Cheney was one of several officials from the George W. Bush administration who acknowledged that Obama had succeeded where they hadn’t in the frustrating, years-long hunt for bin Laden. Bush released a statement saying he had congratulated Obama during a phone call Sunday.

Yet members of the Bush administration — as well as Obama officials — said the prior administration deserved credit, too.

Without information from detainees at the Guantanamo Bay prison and elsewhere, U.S. officials would never have tracked the courier who led them to bin Laden’s compound, they said. Much of the intelligence and logistical groundwork was also laid during the Bush era.

Former Secretary of State Condoleezza Rice called the killing of bin Laden “a tremendous triumph.”

“It says to those that would harm us out there that it takes patience, but we keep working at these issues across administrations, across presidencies, and we will eventually get you,” she said in an interview.

The Obama administration took office strongly opposed to aspects of the Bush administration’s anti-terrorism policy, vowing to prohibit torture during interrogation and to close the detention center at Guantanamo Bay. But under public and political pressure, the Obama team has backed off from shuttering Guantanamo.

Stephen J. Hadley, who was deputy national security adviser on Sept. 11, 2001, and later national security adviser, said the praise for Obama from Republicans was “an indication that on the issue of terrorism, the country really has come together.”

Still, there was some zing in the comments of Bush officials who had been heavily criticized for adopting harsh interrogation techniques and establishing the Guantanamo prison.

Paul D. Wolfowitz, the former deputy secretary of defense, said Monday that “most Republicans have been applauding what [Obama] did.” However, he added, the operation “also rested heavily on some of those controversial policies” instituted by Bush, such as setting up the Guantanamo camp. He spoke in a conference call organized by the American Enterprise Institute.

“All of this was made possible by the relentless, sustained pressure on al-Qaeda that the Bush administration initiated after 9/11 and that the Obama administration has wisely chosen to continue,” former Defense secretary Donald H. Rumsfeld wrote on Facebook.

Juan Zarate, who served as deputy national security adviser for terrorism issues in the second George W. Bush administration, said the carryover of personnel to the Obama administration contributed to the successful effort. For example, Nick Rasmussen, Zarate’s deputy at the National Security Council, is now a deputy to Obama’s chief counterterrorism adviser, John O. Brennan.

“The reality is, there’s been a lot of continuity in our counterterrorism activities,” he said.

Hadley said that in the latter years of the Bush administration, the president directed the intelligence community to work harder at developing human sources and other kinds of information.

“That was a multi-year effort by the intelligence community. It finally came to fruition in the last few months,” he said in an interview.

Some members of the Bush administration could barely contain their joy that the long pursuit of bin Laden was over.

“Justice has been done to Osama bin Laden: all Americans are proud of our military, intel & Presidents Bush, Obama. USA! USA!” tweeted Karl Rove, a former senior adviser to Bush.

But others were more cautious, noting that al-Qaeda was hardly dead. Richard Haass, a senior adviser to then-Secretary of State Colin Powell on 9/11, said he felt “satisfaction that it [the killing] closes something of a chapter.”

But “when I see comparisons to V-E Day. . . . I start getting nervous. It shows a certain misunderstanding of the nature of terrorism,” he said in a conference call arranged by the Council on Foreign Relations.