U.S. President Barack Obama said Monday the world is a better place with Osama bin Laden dead, after DNA evidence confirmed the al Qaeda leader had been killed by an elite team of American military personnel.

Speaking at a Medal of Honour ceremony, where he awarded two soldiers who died in the Korean War, Obama said the world "is a better place because of the death of Osama bin Laden."

Bin Laden died in a firefight with U.S. forces in Pakistan, John Brennan, President Barack Obama's top counterterrorism adviser, said. He had been living inside a large compound.

"Here is bin Laden, who has been calling for these attacks, living in this million-dollar-plus compound, living in an area that is far removed from the front, hiding behind women who were put in front of him as a shield," Brennan told reporters at the White House. "I think it really just speaks to just how false his narrative has been over the years."

The 40-minute operation that took place Sunday was monitored in real-time by Obama and his top officials, but Brennan did not clarify if that meant they were watching live video of the events.

"It was probably one of the most anxiety-filled periods of time in the lives of the people who were assembled here," Brennan said. "The minutes passed like days."

The White House had earlier reported that bin Laden used one of his wives as a human shield before he was killed, but officials later said that was not the case.

It is "inconceivable" that bin Laden did not have some support in Pakistan keeping his location secret, Brennan said.

The compound where bin Laden was found was located less than a kilometre from a military academy that trains top officers in the Pakistani army.

Brennan said the White House is now talking with the Pakistani government. He pledged to pursue all leads to find out what type of support system bin Laden might have had.

As for whether the White House plans to release photos or other hard proof of bin Laden's death, Brennan said that is still "to be determined." Obama administration officials have said they used multiple methods, including DNA evidence, to confirm that the man they killed Sunday was bin Laden.

"We are going to do everything that we can to make sure that nobody has any basis to try to deny that we got Osama bin Laden," Brennan said. "And so therefore, the releasing of photographs and whether that includes photographs, that is something to be determined."

He said U.S. officials have released "a tremendous amount of information" to date, and while he and his team want the world to understand exactly what happened, "we don't want to compromise our ability to be as successful the next time we get one of these guys."

Earlier in the day, Obama said bin Laden's death would not stop al Qaeda's followers from targeting the United States in future.

"There's no doubt that al Qaeda will continue to pursue attacks against us. We must -- and we will -- remain vigilant at home and abroad," he said Monday morning.

U.S. intelligence officials believe bin Laden made a propaganda recording shortly before he was killed and that it will likely surface soon.

They did not make clear whether the tape would be video or audio, but officials said it is likely making its way through al Qaeda's media channel.

An official told The Associated Press the timing of the tape was likely coincidental and bin Laden probably did not know the U.S. was closing in on him.

The RCMP says it is assessing what impact bin Laden's death might have on the threat level in Canada, given the concerns about reprisals against western nations.

The Mounties say they remain vigilant about potential threats to national security and say they will adjust security measures here and at our embassies as needed.

How the raid unfolded

It was Obama who gave the orders for the early-morning raid on a fortified compound in Abbottabad, Pakistan.

A small team of Navy SEALs flew to the compound via helicopter and engaged bin Laden and his supporters in a 40-minute firefight, after the terrorist leader and his guards resisted the attack.

A U.S. official told the Associated Press that two dozen SEALs in night-vision goggles dropped into the high-walled compound in Pakistan by sliding down ropes from Chinook helicopters. The official said that bin Laden went down firing after being hit by a barrage of carefully aimed return fire.

The official spoke on condition of anonymity because aspects of the operation remain classified.

Brennan would not confirm that report. But he did say that the forces who killed bin Laden would have taken him alive if they had had the opportunity. Brennan said the forces were prepared for the "remote" possibility bin Laden would be captured alive. But since he fought back, he was killed.

The SEALs retrieved bin Laden's body and turned the remaining detainees over to Pakistani authorities.

U.S. on bin Laden's trail for months

CTV's Washington Bureau Chief Paul Workman said it appears that the U.S. tracked bin Laden to his final location over a period of a few months.

"Barack Obama went on television last night to say that sometime last year in August, he received word of a lead on the whereabouts of Osama bin Laden -- he put it as deep in Pakistan, inside Pakistan," Workman told CTV's Canada AM from Washington on Monday morning.

"It was pursued, finally there were a number of high-level meetings and yesterday Obama authorized the attack on this compound."

After bin Laden was killed, U.S. forces took custody of his remains, which were taken to the USS Carl Vinson, and officials have privately told reporters he was buried at sea.

An official who spoke to AP said the decision was made to bury bin Laden at sea because Islamic tradition calls for a speedy burial. It was also decided that it would be too difficult to find a country willing to accept the al Qaeda leader's remains.

Obama credits work of American intelligence

In announcing bin Laden's death, Obama gave credit to the Americans who have spent most of the past decade trying to track down the mastermind behind the attacks of Sept. 11, 2001.

Eric Margolis, a journalist and terrorism expert, said the full story behind the Sept. 11 attacks has died with bin Laden, though his divisive agenda will live on.

Speaking with CTV's Canada AM on Monday morning, Margolis said the apparent decision to bury bin Laden at sea "shows how the United States is very concerned that he is a martyr figure and they didn't want his grave to become a shrine."

Across the Pakistan border, Afghan President Hamid Karzai said bin Laden had been dealt his "due punishment," though he said the surprise strike on the Abbottabad compound was proof that the war on terror should focus more outside his country's borders.

French President Nicolas Sarkozy praised "the tenacity of the United States" in its nearly decade-long quest to hunt down bin Laden, while Italian Premier Silvio Berlusconi said his death was a "great result in the fight against evil."

Israeli Prime Minister Benjamin Netanyahu said bin Laden's death was "a resounding victory for justice, for freedom and for the shared values of all democratic countries that fight shoulder to shoulder against terror."

In Saudi Arabia, the government released an official statement saying bin Laden's death will be a "step that support the international efforts against terrorism."

With files from The Associated Press