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U.S. officials and analysts cautioned Thursday that western nations must continue to keep a close eye on Libya following the death of strongman Muammar Qaddafi, with the transition to democracy still in flux, "extremist elements" on the prowl and potentially thousands of weapons on the loose.

Secretary of State Hillary Clinton, who just two days earlier had expressed hope that Qaddafi would be captured or killed so the Libyan people would not have to "fear" him, told Fox News on Thursday that the country still has a tough road ahead.

"I think it would bring a sigh of relief to a lot of Libyans," Clinton told Fox News of Qaddafi's death, noting that Libyans were concerned he would wage a "guerilla war" if he remained at large.

"If it is true, then that is one more obstacle removed," Clinton said. "They have a very steep climb ahead of them ... to try to bring together Libya, build institutions, start on a new path to the future."

Clinton said Qaddafi's death should give Libyans "breathing space" to rebuild their country.

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A U.S. official confirmed to Fox News that Qaddafi is dead. Earlier, Vice President Biden said Libya has "gotten rid of a dictator."

"Today we can definitively say that the Qaddafi regime has come to an end," President Obama said in an address at the Rose Garden.. "This is a momentous day in the history of Libya."

Obama, said of Libyans, "You have won your revolution."

Obama said the NATO mission would soon be over; if so, the use of a Predator drone Thursday would mark a fitting end for U.S. involvement.

But a U.S. official told Fox News that those involved with the operation have to be "careful that what comes next" isn't worse than Qaddafi. The challenge, the official said, is ensuring "extremist elements" within the anti-Qaddafi forces don't take control and allow the country to become yet another safe haven for terrorists or a source of black-market weapons.

The U.S. has been on alert in recent weeks over unsecured weapons in the wake of Qaddafi's ouster -- particularly 20,000 shoulder-launched missiles.

Former U.S. ambassador to the U.N. John Bolton said securing the weapons should be a "very urgent priority" right now.

"This is certainly not the end of the struggle. It's the end of Qaddafi and that's a good thing," he said.

Obama attended a meeting with national security advisers Thursday morning. It was a previously scheduled meeting, but one official said Libya will be the foremost topic.

Obama endured criticism from both sides of the aisle for launching the multi-national campaign to protect Libyans from Qaddafi back in March, when Qaddafi decided to fight protesters emboldened by gains elsewhere in the Arab world during the Arab Spring. His administration faced complaints from Congress for not seeking lawmakers' explicit permission early on -- some also questioned his strategy of eventually letting the U.S. take a backseat in the operation.

Officials and analysts roundly hailed Qaddafi's death Thursday as welcome news, while those who supported the operation warned the hard work has just begun.

"I think it's closure," Sen. Marco Rubio, R-Fla., told Fox News. Rubio said the U.S. has an important role to play going forward in working with the new Libyan government to ensure stability, disarm the militias and secure loose weapons.

Sen. John McCain, R-Ariz., a supporter of the operation who traveled to Libya to meet with rebels during the height of fighting, said the death "marks an end to the first phase of the Libyan revolution."

"Now the Libyan people can focus all of their immense talents on strengthening their national unity, rebuilding their country and economy, proceeding with their democratic transition, and safeguarding the dignity and human rights of all Libyans," he said in a statement. "The United States, along with our European allies and Arab partners, must now deepen our support for the Libyan people, as they work to make the next phase of their democratic revolution as successful as the fight to free their country."

Former CIA officer Mike Baker said the next phase is probably "the most important part" for Libya's future.

He said the new government has to prevent retribution attacks against pro-Qaddafi forces. Plus he cautioned that the eastern part of Libya has been a "recruiting ground" for Al Qaeda for years, as analysts urged the Obama administration to carefully monitor the "radical" elements among new leaders in Tripoli.

"Many of the big issues facing Libya remain," Bolton said.

Fox News' Wendell Goler and Mike Levine contributed to this report.