He said that was his intention, regardless of whether defiant leader Moamar Gaddafi holds on to power, as allied air strikes continue on Libya's air defences and tanks.
On the last leg of his Latin American tour in El Salvador, Mr Obama was again confronted with the apparent conflict between the broader American commitment to regime change in Libya and the limited UN mandate to protect civilians.
"Unless he is willing to step down, then there are still going to be potential threats towards the Libyan people and we will continue to support the efforts to protect the Libyan people," he said. "But we will not be in the lead."
He said he had spoken with the French and British leaders and had "absolutely no doubt" America would be able to hand over control, saying he expected to see a meeting of the minds over the next several days.
In the face of continuing criticism back home, Mr Obama called the prime ministers of Turkey and Britain and French president Nicolas Sarkozy to lock in support for a quick US handover.
But NATO countries are still struggling to agree on a new command structure, with Italy threatening to withdraw the use of its air bases and France concerned about a negative Arab reaction to a possible NATO takeover.
"I would expect that over the next several days we will have clarity and a meeting of the minds of all those who are participating in the process," Mr Obama said.
"We are already seeing a significant reduction in the number of US planes that are involved in operations over Libya."
Ahead of a likely frosty reception from congressional leaders over his proceeding without consulting them first, Mr Obama appealed directly to the American people, saying that US forces had saved lives and that if he had not acted there could have been a humanitarian catastrophe in the rebel-held city of Benghazi.
He said the mission is limited, well-defined and can be afforded despite the US government's ballooning debt problem.
"I said at the outset that this was going to be a matter of days and not weeks," he said.
"And there's nothing based on how we've been able to execute over the last several days that changes that assessment."
But Mr Obama acknowledged the danger of a stalemate - that when the UN mission is completed Mr Gaddafi could still be in power.
'Reaching out'
Meanwhile, US secretary of state Hillary Clinton has suggested that Mr Gaddafi might be considering his own exit strategy.In an interview with America's ABC News, Ms Clinton suggested that people close to Mr Gaddafi, and perhaps the leader himself, could be looking for a way out.
"We've heard about other people close to him reaching out to people that they know around the world - Africa, the Middle East, Europe, North America, beyond - saying, 'What do we do? How do we get out of this? What happens next?'," she said.
"I'm not aware that he [Mr Gaddafi] personally has reached out, but I do know that people allegedly on his behalf have been reaching out."
But the defiant leader has appeared on Libyan television, calling for an Islamic army to stand up against the West.
"All the Muslim armies have to take part in this battle against the crusader," he said.
"There are protests all over the world in support of you - in Asia, in Africa, in America, in Europe.
"Their people are against their own leaders.
"We will win. We will be victorious in this historical battle. We will not surrender."
Foreign reporters were told he was speaking from his Tripoli compound to supporters who had formed a human shield to protect him.
He vowed to stay and his speech was followed by a fireworks display.
Fighting continues
As allied countries decide who will take command of the military operation to police a no-fly zone and protect civilians, anti-Gaddafi rebels are struggling to capitalise on air strikes against Libyan tanks and air defences.Government forces have attacked two west Libyan towns, killing dozens, while rebels were pinned down in the east.
In the latest fighting, Mr Gaddafi's tanks shelled the rebel-held western town of Misrata and casualties included three children killed when their car was hit, residents said, adding the death toll for Monday alone had reached 40.
Residents painted a grim picture of the situation in Misrata, under siege by Gaddafi loyalists for weeks, with tanks in the city centre and doctors operating on people with bullet and shrapnel wounds in hospital corridors.
"The situation here is very bad. Tanks started shelling the town this morning," a resident called Mohammed said by telephone from outside the city's hospital.
"Snipers are taking part in the operation too. A civilian car was destroyed killing three children on board, the oldest is aged 13 years."
In the first Western air force loss of the campaign, a US F-15 crashed in Libya. Two crew on board the fighter jet at the time were rescued.
The crash was likely to have been caused by mechanical failure and not hostile fire, the US military said.
Explosions and anti-aircraft fire have reverberated across Tripoli for the past three nights and state television reported several attacks by the "crusader enemy".
Twenty Tomahawk missiles were fired at Libyan targets overnight, the US military said.
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