"I believe that we have built enough momentum that as long as we sustain the course we're on, he will step down," the visiting president said at a joint news conference with British Prime Minister David Cameron.
"Ultimately this is going to be a slow, steady process in which we're able to wear down the regime forces," Obama said. He ruled out a deadline for ending the U.S. role in Libya, saying the mission would end in a timely fashion
Cameron rallied behind Obama's approach, saying what was needed in Libya was "patience and persistence."
The two leaders affirmed their joint resolve despite complaints among some NATO countries about the reduced U.S. role since NATO took the lead after the initial days of the two-month-old campaign against Gadhafi.
But the president also said, "David and I both agree that you can't put boots on the ground in Libya." He said "enormous sacrifices" made by the NATO allies have made a difference, but that ultimately "this is going to be a slow, steady process" that eventually will sap Gadhafi's resolve.
"We've been extraordinarily successful in avoiding civilian casualties," Obama added. "That means that sometimes we may have to be more patient than people would like."
Said Cameron: "I would agree that the two key things here are patience and persistence." He said "we're extremely strong together in wanting to see the same outcomes."
France among other NATO countries has pushed for a more aggressive military approach in Libya, but Obama gave no indication that increased firepower would be forthcoming from the U.S. even though officials in some allied nations would like to see that.
At the same time, the president said the U.S. is "strongly committed to seeing the job through, making sure that, at a minimum, Gadhafi doesn't have the capacity to send in a bunch of thugs to murder innocent civilians and to threaten them."
The international community has stepped up both the air campaign and diplomatic efforts against the regime in a bid to break a virtual stalemate between the rebels in the east and Gadhafi, who maintains a stranglehold on most of the west.
The military campaign in Libya began with what seemed a narrowly defined mission: to enforce a no-fly zone and protect civilians from attack. Two months later, the campaign has evolved into a ferocious pounding of the country's capital, Tripoli, in what appears an all-out effort to oust Gadhafi. But that goal remains elusive.
The Libyan opposition remains weak. NATO, the North Atlantic military alliance which took over command of the campaign from the U.S. on March 31, appears to have no clear exit strategy. Two of the allies, Britain and France, have descended into public squabbling over bringing the fight closer to Gadhafi with attack helicopters. And the French foreign minister said Tuesday his country's willingness to continue the campaign was not endless.
On another matter, Obama said the U.S. is increasing pressure on Syria's President Bashar Assad and his regime, which has been attacking protesters there.