President Obama warned Libyan leader Muammar al-Qaddafi that the NATO military campaign against his regime "will not relent," as both he and British Prime Minister David Cameron reaffirmed their commitment to the mission and called on Qaddafi to leave power.

The president defended the mission, which is in its third month, during a press conference Wednesday with the prime minister and afterward during an address to both houses of the British Parliament. He stressed during his speech that freedom in Libya "must be won by the people," but pledged U.S. support as long as Libyans are threatened by Qaddafi's forces.

"We will not relent until the people of Libya are protected, and the shadow of tyranny is lifted," Obama said.

The strong statements come as lawmakers on Capitol Hill in Washington prepare to challenge U.S. involvement in the North African country. U.S. lawmakers are introducing measures to restrict funding for the mission and require Obama to seek permission from Congress to stay in Libya.

But Obama, in London on a visit to Britain and several other countries, said the operation -- which he described as a "slow, steady process" -- will continue until Qaddafi stops attacking the Libyan people. Obama said he would not place an "artificial timeline" on the mission, but said he's convinced Qaddafi will ultimately step down.

"Time is working against Qaddafi and he must step down from power and leave Libya to the Libyan people," Obama said during the earlier press conference. He claimed the U.S. and its allies are making "enormous progress" and have "saved lives" since entering Libya in March. "There will not be a let-up in the pressure that we are applying."

Both leaders appealed to their people for patience with the mission. Cameron said both leaders also agreed on the need to be "turning up the heat" in that country.

"It is not a time for us to shrink back and think about our own issues and interests. This is our issue and this is massively in our interest," Cameron said. "It is impossible to imagine a future for Libya with Qaddafi still in power -- he must go."

The two spoke at a press conference following a private meeting at the prime minister's residence at 10 Downing Street.

The U.S. president faced a host of knotty problems to work through with his British counterpart, including troop levels in Afghanistan and disagreements over the NATO-led bombing campaign in Libya. His larger mission, though, was to reassure European allies that they still are valued partners in a U.S. foreign policy that increasingly looks to Asia.

Obama said at the top of his address that the U.S.-U.K. relationship is one of the strongest "the world has ever known," and that he was in Britain to "reaffirm" that historic bond.

The president acknowledged that growing nations like China, India and Brazil have shaken up the "international order," but said the United States and Great Britain must continue to lead, calling their alliance "indispensable" to the goal of a peaceful and prosperous world.

"The time for our leadership is now," Obama told Parliament.

The two leaders also meet at a time of great financial strain in Europe, with countries including Britain slashing spending in order to get their deficits under control. Mindful of the deficit debate happening back home, Obama lent his support to the spirit of deficit reduction, while stopping short of supporting specific policies. He said government aid for the sick and unemployed continues to be critical.

"Having come through a terrible recession, our challenge is to meet these obligations while ensuring that we're not ... consumed with a level of debt that could sap the strength and vitality from our economies," Obama said in his address.

"Barack and I did not come into politics to cut public spending, but neither did we seek office to see our great economies decline and to land our children with unsustainable debt," Cameron said Wednesday during their press conference.

There were also lighter duties Wednesday, as Obama and Cameron capped their bilateral meetings by rolling up their sleeves to flip burgers at a barbecue hosted by their wives to honor the sacrifices of their militaries. Dozens of active-duty troops from the U.S. and Britain, along with some spouses, attended the event in the backyard of 10 Downing, underscoring a partnership just announced between the two countries to share resources to help service members and their families.

On Libya, some British lawmakers say Britain and France have shouldered an unfair burden in the campaign and are calling on the U.S. to deploy additional planes to increase the pace of airstrikes.

The White House, however, said it has no plans to increase its footprint in the Libya mission.

The White House said Obama would discuss with Cameron ways the international community can boost its support for the Libyan opposition, including funneling them money from frozen Qaddafi assets. There is also keen interest in Britain over U.S. plans to withdraw forces in Afghanistan. Obama is expected to announce the first phase of the withdrawal within weeks, and British military officials have said they will support whatever decision Obama makes. Britain has 10,000 troops in Afghanistan, second only to the 100,000 U.S. forces there.

Obama began his two-day stop in London with a grand royal welcome from Queen Elizabeth II. The president and his wife, Michelle, were greeted in an elaborate ceremony at Buckingham Palace and toasted at a lavish banquet held in their honor.

The Obamas are staying at the palace while in London as guests of the queen, who is said to have taken a liking to the American couple.

From England Obama will travel Thursday to France for an economic summit, before ending his trip in Poland. He returns to Washington Saturday night, and on Sunday heads to Missouri to view damage from the devastating tornadoes there.

The Associated Press contributed to this report.