President warns other Middle Eastern dictators, particularly Syrian president Bashar al-Assad, that they could be next

President Barack Obama hailed the lifting of the "dark tyranny" over Libya after the new government confirmed Muammar Gaddafi had been killed, issuing a warning to other dictators in the Middle East – and particularly Syria – that they could be next.

Although Obama did not name Syrian president Bashar al-Assad, it was he Obama had in mind when he said the rule of the iron fist in the Middle East is inevitably coming to an end. Those leaders that try to deny the push for democracy will not succeed, he predicted.

Obama was speaking in the White House Rose Garden after footage was shown worldwide of what appeared to be Gaddafi's bloody corpse. "One of the world's longest-serving dictators is no more," the president said.

The Libyans had won their revolution and "the dark shadow of tyranny has been lifted," Obama said.

Given the number of false claims in recent weeks that Gaddafi had been killed or captured, Obama was careful not to say categorically that he was dead.

Instead, he confined himself to a carefully chosen formula: "We can definitively say the Gaddafi regime has come to an end."

He promised US help for Libya in establishing an interim government and in the holding of fair and free elections, but anticipated "difficult days ahead".

The death of Gaddafi immediately raised speculation in the US that the same military model – the use of US air power combined with rebel forces on the ground and special forces from Europe – could be used again in Syria.

Vice-president Joe Biden described the military model as a "prescription" for the future, while White House spokesman Jay Carney, when asked about Syria, said Assad had lost his legitimacy to rule.

The former Nato commander, Wesley Clark, asked if the same strategy could be used in Syria, replied: "Could be." He told CNN that every country had to be approached differently: "Syria is going to be different from Libya, but it shows Nato is capable of a sustained effort."

Obama, facing re-election next year, chalked up Libya as another foreign policy success to place alongside the killing in May of al-Qaida leader Osama bin Laden, the drawdown of most US troops from Iraq by the end of the year, and the first phase of a gradual pullout of troops from Afghanistan.

Secretary of state Hillary Clinton was caught on camera saying "wow" when shown a report that Gaddafi had been captured, though she immediately composed herself, adding it was unconfirmed.

Later, interviewed by CNN, Clinton said that if Gaddafi were still at large, it would have created continuing security problems because "he would try to marshal support, that he would pay for mercenaries, that he would engage and effect guerrilla warfare. So if he's removed from the scene, there may still be those who would do so, but without the organising figure of Gaddafi, and that makes a big difference."

Obama was criticised at the outset of the Libyan revolution by Republicans for being too slow to intervene, and by Democrats worried he was taking the US into another war. He faced opposition too from his then defence secretary, Robert Gates, now retired, who was reluctant to become engaged in another war, but Obama and Clinton overruled him. Gates at least won the argument that no US ground troops would be committed.

Obama's approach to Libya was to provide US air power in support of the rebels but not putting US troops on the ground, leaving that to other countries, mainly France and Britain.

In the Rose Garden, he basked in his success: "Without putting a single US service member on the ground, we achieved our objectives, and our Nato mission will soon come to an end."

Biden, speaking hours before Obama, adopted a clearly partisan approach to news of the dictator's death, bluntly contrasting the apporach of the Obama administration to Libya with George Bush's in Iraq.

"In this case, America spent $2bn total and didn't lose a single life. This is more of the prescription for how to deal with the world as we go forward than it has been in the past," he said, out on the campaign trail in New Hampshire.

He added that the the Obama administration had made the right decision in taking a secondary role to Britain and France in Libya.

Gaddafi is alleged to have been behind the Lockerbie bombing in 1988, and some of the the US families of those killed welcomed his death.

The Obama administration now faces a dilemma over whether to push for the Libyan convicted of the Lockerbie bombing, Abdelbaset al-Megrahi, to be brought to the US. He was released from a Scottish prison after being diagnosed as dying of cancer. But the new Libyan government is reluctant to let him leave the country, and it could undermine the government in its early stages to bow to Washington over this.

The Republican House speaker, John Boehner, appeared to allude to this when he said today: "It is also my hope that the new Libyan government will work to resolve all issues associated with Gaddafi's terrorism-sponsored activities. If they do those things, they will find us a willing friend and partner in the years to come."

Other Republicans in Congress joined in welcoming news of Gaddafi's demise. John McCain, one of the leading foreign affairs specialists in the Senate, and Obama's opponent in the 2008 White House election, described Gaddafi's death as "an end to the first phase of the Libyan revolution", and urged increased US support for the fledgling Libyan government.

The Democratic chairman of the Senate foreign relations committee, John Kerry, a close ally of the president, said the US had "demonstrated clear-eyed leadership, patience and foresight by pushing the international community into action."