WASHINGTON — Declaring the killing of Osama bin Laden “a good day for America,” President Barack Obama said Monday the world was safer without the al-Qaida terrorist and mastermind of the Sept. 11, 2001 attacks. His administration used DNA testing to help confirm that American forces in Pakistan had in fact killed bin Laden, as U.S. officials sought to erase all doubt about the stunning news.

A U.S. official says Osama bin Laden went down firing at the Navy SEALs who stormed his compound.

“Today we are reminded that as a nation there is nothing we can’t do,” Obama said of the news bound to lift his political standing and help define his presidency. He hailed the pride of those who broke out in overnight celebrations as word spread around the globe.

An elite crew of American forces killed bin Laden during a daring raid on Monday, capping the world’s most intense manhunt, a search that spanned nearly a decade.

Bin Laden was shot in the head during a firefight and then quickly buried at sea. White House officials were mulling the merits and appropriateness of releasing a photo.

As spontaneous celebrations and expressions of relief gave way to questions about precisely what happened and what comes next, U.S. officials warned that the campaign against terrorism is not nearly over — and that the threat of deadly retaliation against the United States and its allies was real.

Senior administration officials said the DNA testing alone offered near 100 percent certainty that bin Laden was among those shot dead. Photo analysis by the CIA, confirmation by a woman believed to be bin Laden’s wife on site, and matching physical features like bin Laden’s height all helped confirmed the identification.

“We can all agree this is a good day for America,” a subdued Obama said during a Medal of Honor ceremony in the glimmering White House East Room.

Still, it was unclear if the world would ever get visual proof.

Senior U.S. officials said bin Laden was killed toward the end of the firefight, which took place in a building at a compound north of Islamabad, the Pakistani capital. His body was put aboard the USS Carl Vinson and placed into the North Arabian Sea.

An official familiar with the operation said bin Laden fired on U.S. forces and was hit by a barrage of carefully aimed return fire.

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

The official says two dozen SEALs in night-vision goggles dropped into the high-walled compound in Pakistan by sliding down ropes from Chinook helicopters in the overnight raid.

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

Traditional Islamic procedures for handling the remains were followed, the officials said, including washing the corpse, placing it in a white sheet.

Across the government, Obama’s security team used the occasion to warn that the campaign against terrorists was hardly over.

“The fight continues and we will never waver,“ Secretary of State Hillary Rodham Clinton said Monday. Her comments had echoes of former President George W. Bush’s declaration nearly a decade ago, when al-Qaida attacks against America led to war in Afghanistan and changed the way Americans viewed their own safety.

Turning to deliver a direct message to bin Laden’s followers, she vowed: “You cannot wait us out.“

U.S. Capitol Police put on a conspicuous show of force Monday morning with 10 vehicles amassed near Constitution Avenue with their lights flashing and doors and trunks open. Officers armed with automatic weapons kept watch on every vehicle that passed.

Obama himself had delivered the news of bin Laden’s killing in a dramatic White House statement late Sunday. “Justice has been done,” he declared.

Officials say CIA interrogators in secret overseas prisons developed the first strands of information that ultimately led to the killing of bin Laden.

The military operation that ended his life took mere minutes, and there were no U.S. casualties.

U.S. Blackhawk helicopters ferried about two dozen troops from Navy SEAL Team Six, a top military counter-terrorism unit, into the compound identified by the CIA as bin Laden’s hideout — and back out again in less than 40 minutes. Bin Laden was shot after he and his bodyguards resisted the assault, officials said.

Three adult males were also killed in the raid, including one of bin Laden’s sons, whom officials did not name. One of bin Laden’s sons, Hamza, is a senior member of al-Qaida. U.S. officials also said one woman was killed when she was used as a shield by a male combatant, and two other women were injured.

The compound is about a half-mile from a Pakistani military academy, in a city that is home to three army regiments and thousands of military personnel. Abbottabad is surrounded by hills and with mountains in the distance.

Critics have long accused elements of Pakistan’s security establishment of protecting bin Laden, though Islamabad has always denied it, and in a statement the foreign ministry said his death showed the country’s resolve in the battle against terrorism.

Bin Laden’s death came 15 years after he declared war on the United States. Al-Qaida was also blamed for the 1998 bombings of two U.S. embassies in Africa that killed 224 people and the 2000 attack on the USS Cole that killed 17 American sailors in Yemen, as well as countless other plots, some successful and some foiled.

“We have rid the world of the most infamous terrorist of our time,” CIA director Leon Panetta declared to employees of the agency in a memo Monday morning. He warned that “terrorists almost certainly will attempt to avenge” the killing of a man deemed uncatchable. “Bin Laden is dead. Al-Qaida is not,” Panetta said.

Retaliatory attacks against the U.S. and Western targets could come from members of al-Qaida’s core branch in the tribal areas of Pakistan, al-Qaida franchises in other countries, and radicalized individuals in the U.S. with al-Qaida sympathies, according to a Homeland Security Department intelligence alert issued Sunday and obtained by The Associated Press.

While the intelligence community does not have insight into current al-Qaida plotting, the department believes symbolic, economic and transportation targets could be at risk, and small arms attacks against other targets can’t be ruled out.

In all, nearly 3,000 were killed in the Sept. 11 attacks.

As news of bin Laden’s death spread, hundreds of people cheered and waved American flags at ground zero in New York, the site where al-Qaida hijacked jets toppled the twin towers of the World Trade Center. Thousands celebrated all night outside the White House gates.

Many people said they were surprised that bin Laden had finally been found and killed. John Gocio, a doctor from Arkansas who was gathering what details he could from TV screens at O’Hare Airport in Chicago, marveled: “After such a long time, you kind of give up and say, ‘Well, that’s never going to happen.’ “

A couple of people posed for photographs in front of the White House while holding up front pages of Monday’s newspapers announcing bin Laden’s death.

The development seems certain to give Obama a political lift. Even fierce critics such as former Vice President Dick Cheney praised him.

But its ultimate impact on al-Qaida is less clear.

The greatest terrorist threat to the U.S. is now considered to be the al-Qaida franchise in Yemen, far from al-Qaida’s core in Pakistan. The Yemen branch almost took down a U.S.-bound airliner on Christmas 2009 and nearly detonated explosives aboard two U.S. cargo planes last fall. Those operations were carried out without any direct involvement from bin Laden.

The few fiery minutes in Abbottabad followed years in which U.S. officials struggled to piece together clues that ultimately led to bin Laden, according to an account provided by senior administration officials who spoke on condition of anonymity because of the sensitivity of the operation.

Based on statements given by U.S. detainees since the 9/11 attacks, they said, intelligence officials have long known that bin Laden trusted one al-Qaida courier in particular, and they believed he might be living with him in hiding.

Four years ago, the United States learned the man’s identity, which officials did not disclose, and then about two years later, they identified areas of Pakistan where he operated. Last August, the man’s residence was found, officials said.

“Intelligence analysis concluded that this compound was custom built in 2005 to hide someone of significance,” with walls as high as 18 feet and topped by barbed wire, according to one official. Despite the compound’s estimated $1 million cost and two security gates, it had no phone or Internet running into the house.

By mid-February, intelligence from multiple sources was clear enough that Obama wanted to “pursue an aggressive course of action,” a senior administration official said. Over the next two and a half months, the president led five meetings of the National Security Council focused solely on whether bin Laden was in that compound and, if so, how to get him, the official said.

Obama made a decision to launch the operation on Friday, shortly before flying to Alabama to inspect tornado damage, and aides set to work on the details.

Administration aides said the operation was so secretive that no foreign officials were informed in advance, and only a small circle inside the U.S. government was aware of what was unfolding half a world away.