The splintered coalition of nations engaged in a four-week-old air campaign over Libya struggled Wednesday to come up with new tactics to topple Moammar Gaddafi without resorting to further Western engagement in Libya’s back-and-forth civil war.

President Nicolas Sarkozy of France, the vanguard of intervention in favor of rebel forces, met at the Elysee Palace with British Prime Minister David Cameron. The two leaders have been the main actors in the NATO-led air war since the United States handed over leadership March 31 and pulled back most of its aircraft into a support role.

Their goal, a British official said, was to find ways to persuade other NATO nations to invest more aircraft and political capital in the bombing campaign, now being shouldered overwhelmingly by British and French warplanes. Although more than 175 aircraft from 17 nations have joined the coalition, most governments have surrounded their participation with restrictions that prevent them from carrying out effective strike missions against Gaddafi’s forces.

“Clearly, there is a belief that NATO could do more in terms of direct support,” said the British official, speaking on the condition of anonymity because of the sensitivity of the subject.

As Cameron and Sarkozy huddled here, envoys from 20 nations gathered in Qatar, on the Persian Gulf, to lay groundwork for an accelerated push for a diplomatic solution to the Libya conflict. The NATO secretary general, Anders Fogh Rasmussen, reminded the diplomats that NATO’s mission is to protect civilians, not win the war for rebel forces, and he declared that ultimately there is not a purely military solution.

As long as Gaddafi remains in Libya at the head of a loyalist army, however, it was difficult to see where the diplomacy was leading, specialists in Paris noted. Rebel leaders have vowed not to lay down their arms until Gaddafi and his sons are gone.

In the meantime, representatives of the rebels’ Transitional National Council at the meeting in Qatar called for more intensive NATO airstrikes, particularly against Libyan army tanks and missile batteries involved in attacks against the rebel-held cities of Misurata, 131 miles east of Tripoli, the capital, and Ajdabiya, 99 miles south of rebel headquarters in Benghazi.

The efforts to enforce a no-fly zone over Libya also will top the agenda for a two-day meeting of NATO foreign ministers that begins in Berlin Thursday.

The Obama administration continued to push back on the suggestion that more U.S. military help was needed. Pentagon officials acknowledged that U.S. aircraft have been flying a small number of combat missions all along — mainly to suppress Libyan air defenses — while leaving the bulk of the flying to allies. But the officials said there have been no specific requests from NATO to bring back more U.S. warplanes.

Likewise, a State Department spokesman said Wednesday that there were as yet no plans for further U.S. military involvement.

“We believe that this operation’s been successful and that, led by NATO, it can continue to be successful,” the spokesman, Mark Toner, told reporters in Washington. Warplanes were protecting civilians and allowing diplomats and others to tackle the separate goal of persuading Gaddafi to leave, he said.

U.S. officials acknowledged that the alliance members who were doing the bulk of the combat missions wanted to see others take on a greater role. “There’s a constant conversation going on about . . . how burdens can be shared,” said a U.S. official familiar with planning for the air campaign. “As this takes on a longer character, the question is — at what point are other countries going to take up some of the slack and some of the burden?”

In addition to France and Britain, the countries participating in the airstrikes are Norway, Canada, Denmark and Belgium. U.S. teams are doing virtually all the surveillance and reconnaissance — and thus are chiefly responsible for targeting, without physically dropping bombs. Seven nations are patrolling Libyan airspace to enforce the no-fly zone: the Netherlands, Sweden, Spain, Italy, Qatar, Jordan and the United Arab Emirates. Turkish airplanes are helping to enforce the arms embargo outside Libya.

Adding more strike aircraft would not necessarily lead to a great increase in the tempo of the air campaign, said the U.S. official, who insisted on anonymity in discussing sensitive details of the international operation. “It isn’t like there are hundreds of targets not being struck because there’s not enough capability. Anything we see, we strike,” the official said.

Although the U.N. Security Council resolution authorizing NATO intervention addressed protecting civilians, French, British, U.S. and other officials have from the beginning made it clear their objective is Gaddafi’s defeat. French Foreign Minister Alain Juppe, addressing reporters in Doha, the Qatari capital, again emphasized that was France’s aim in calling for reinforcements in the air campaign.

A statement issued at the end of the Doha meeting, in effect endorsing the rebel cause, also emphasized that Gaddafi’s departure is a precondition to any attempt at resolving the conflict.

Italy, which has made its air bases available for the battle against Gaddafi, said Western nations should go a step further and supply what officials called “defensive weapons” to the Benghazi-based rebel forces in northeast Libya. Maurizio Massari, a spokesman for Foreign Minister Franco Frattini, did not explain the distinction between defensive and offensive arms. In the seesaw combat that has raged around Libyan cities for nearly two months, both sides have used automatic rifles, machine guns mounted on pickups, rocket launchers and ground-to-ground missiles to attack enemy positions and defend their own.

But Belgian Foreign Minister Steven Vanackere objected to the proposal in any case, saying the Security Council resolution authorized protecting civilians “but not arming them.”

His comment underscored how the ambiguity surrounding NATO’s campaign has contributed to difficulties in carrying it out. On one hand, France and Britain have interpreted the resolution broadly as a license to help the rebels force Gaddafi from power by military means. But on the other hand, some governments have interpreted it more restrictively, saying they will only help enforce a no-fly zone and prevent the army from massacring civilians.

British Foreign Secretary William Hague proposed, meanwhile, that a “regional financial mechanism” be set up to get funds to the rebel leadership in Benghazi. He said the mechanism — in effect, a channel for wealthy gulf countries to donate money — would allow the Transitional National Council to provide basic services to people living in rebel-held areas and assist the growing numbers of Libyans displaced by the fighting.

The U.N. secretary general, Ban Ki-moon, estimated that as many as 3.6 million of Libya’s 6 million inhabitants will need humanitarian aid of one kind or another. The fate of civilians among Misurata’s 300,000 inhabitants has been particularly worrying, with reports from the city describing wounded who cannot be tended to and lack of electricity or water at medical facilities.

Some aid ships have entered the Misurata and Benghazi ports, and French officials reported a government-chartered plane landed in Benghazi on Wednesday with 10 tons of medicine and a team of medical volunteers. But the need is acute for much more, rebel leaders said. Overall, they added, about 10,000 rebel fighters and civilians have been killed, 30,000 wounded and 20,000 listed as missing since the conflict erupted.

Correspondent Anthony Faiola in London and staff writers Joby Warrick and Karen DeYoung in Washington contributed to this report.