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Carolyn Kaster, Associated Press
President Barack Obama and Britain's Prime Minister David Cameron participate in a joint news conference at Lancaster House in London, Wednesday, May 25, 2011.

LONDON — Firmly united against Moammar Gadhafi, President Barack Obama and Prime Minister David Cameron promised a relentless and punishing pummeling of his forces in Libya on Wednesday but also pleaded for patience for an effort with no clear end in sight. Obama ruled out a deadline for ending NATO's military assault, saying only that it would be over "in a timely fashion."

"Gadhafi and his regime need to understand that there will not be a let-up in the pressure that we are applying," the U.S. president said, even as Libyan rebels clashed with mercenaries fighting for Gadhafi and less than a day after NATO intensified its bombardment of the Libyan capital. Britain's leader, hosting a news conference with Obama, said the two agreed on a need to "be turning up the heat in Libya."

The Libyan crisis and the broader Arab uprisings across North Africa and the Middle East will be major topics as Obama, Cameron and leaders of other wealthy nations head to the Group of Eight gathering in the Normandy resort of Deauville, France, for talks that begin Thursday. The world's top economies are scrambling to figure out how to help countries with democratic transitions without being seen as heavy-handed.

For Obama and Cameron, the bullish language on Gadhafi came as the international community has stepped up both the air campaign and diplomatic efforts against him in a bid to break a virtual stalemate between the rebels in the east of Libya and Gadhafi, who maintains a stranglehold on most of the west.

The NATO mission, authorized by a United Nations mandate, is intended to save lives but not to create a regime change — as Cameron reminded everyone on Wednesday.

In essence, however, Gadhafi has become a target, as has his presidential compound. NATO's official line is that the compound is a command-and-control center and that it is not trying to kill Gadhafi.

Away from Tripoli, Libyan rebels clashed Wednesday with Sudanese mercenaries fighting for Gadhafi near the border with Sudan. Gadhafi has long provided arms, training and vehicles to various rebel groups in Sudan.

The resolve and political will of the nations involved in challenging Libya's government are being tested as Gadhafi remains entrenched.

"I believe that we have built enough momentum that as long as we sustain the course that we're on, that he is ultimately going to step down," Obama said. He refused to say how long that would take, calling any such timeline artificial. But he added that if the coalition shows resolve and pours in resources, "we're going to be able to achieve our mission in a timely fashion."

"The two key things here are patience and persistence," Cameron added.

Neither is in huge supply in the United States given that the U.S.-led wars in Iraq and Afghanistan have raged on for years.

The U.S. and British leaders said that Gadhafi has seen his military power and grip on the country degraded since this campaign began, under United Nations authority, as an emergency effort to protect the civilians who have been challenging him. The United States and Britain remain adamant that they will not send in ground forces even as the try to support the rebels other ways.

"Ultimately this is going to be a slow, steady process in which we're able to wear down the regime forces," Obama said. Pushing back against those who may question the success of the effort, Obama raised the prospect of some false perception that NATO had some secret air assets it wasn't employing, and then he shot it down.

"Once you rule out ground forces, then there are going to be some inherent limitations to our air strike operations," Obama said. "It means that the opposition on the ground in Libya is going to have to carry out its responsibilities."

That opposition remains weak. And NATO, the North Atlantic military alliance that 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, something France plans to do but that Cameron avoided addressing directly when asked Wednesday.

Libyan government spokesman Moussa Ibrahim reacted angrily to Obama's assertion that Gadhafi should leave power against the threat of a relentless campaign.

"Gadhafi's destiny, Gadhafi's future, is for the Libyan nation to decide," Ibrahim said. "It would be a much more productive statement to say that the Libyan people need to engage in an inclusive, peaceful, democratic, transparent, political process in which they can chose the shape of their political system and the leaders of their system," he said.

On the other hand, rebel media spokesman Jalal Gallal said Obama's statement was "very positive news. We are on the same wavelength."

"We all are agreed in a vision of a democratic Libya without Gadhafi, his family or any member of his inner circle. We also concur that there will be no foreign troops on the ground. We need the international community, the air cover, until the objective is met, and that we have. It is just going to take a little longer than necessary."

He repeated the rebels' call for heavy weapons to match Gadhafi's arsenal: "Given the right equipment and training, we can do the job ourselves."

Witnesses in Libya have reported African mercenary fighters shooting at protesters or being captured by anti-Gadhafi forces. Some were flown in to put down the rebellion, but most fighters were already in the war-torn country.

Meanwhile, in NATO airstrikes overnight, British aircraft hit four of Gadhafi's armored vehicles near the Libyan city of Zlitan, British military spokesman Maj. Gen. John Lorimer said in a statement. Tornado and Typhoon jets also destroyed a radar station in the coastal city of Brega during the Tuesday night raid.

Libya's deputy foreign minister, Khaled Kaim, called on the South African leader Jacob Zuma to push forward negotiations to end the three-month conflict when he arrives next week in Tripoli.

Zuma is the highest-ranking politician to visit Gadhafi since the fighting began in Libya.

Kaim told The Associated Press the Gadhafi government is hoping Zuma will help arrange a cease-fire between Libyan government forces, NATO and the rebels, and oversee a transitional period.

Citing a deep mistrust of Gadhafi and emboldened by NATO strikes, the rebels have insisted Gadhafi must leave power before any negotiations can take place.

Throwing into doubt the effectiveness of Zuma's visit, the South African leader will not be meeting representatives of the interim government based in the de-facto rebel capital of Benghazi.

Kaim said there was no need for Zuma to consult the interim government, on grounds it does not represent most of the rebel insurgents currently battling Gadhafi's forces.

Associated Press writers Michelle Faul in Benghazi, Libya and Diaa Hadid in Tripoli, Libya contributed to this report.