President Obama, outlining his vision for ending the war in Afghanistan, vowed Wednesday to withdraw all surge troops by next summer and declared that after a decade of fighting "the tide of war is receding."

In a prime-time address from the East Room of the White House, the president assured the nation that the U.S. military will begin its drawdown next month from a "position of strength" following the death of Usama bin Laden. He described that drawdown as "the beginning, but not the end, of our effort to wind down this war" -- a transition he wants complete by 2014.

"We have put Al Qaeda on a path to defeat, and we will not relent until the job is done," the president said.

As anticipated, the president called for 10,000 troops to be withdrawn by the end of this year. He said the rest of the surge troops, or about 23,000 will be removed by the end of summer in 2012. It is expected that all surge troops will be out of Afghanistan by September next year.

The president, in framing the drawdown, tried to appeal to competing factions on Capitol Hill and elsewhere over the war. To those urging the president to cut the mission short and withdraw forces at a more rapid pace, Obama affirmed that his interest is "nation-building here at home," not in Afghanistan.

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"We won't try to make Afghanistan a perfect place. We will not police its streets or patrol its mountains indefinitely," he said.

But to those concerned the impending withdrawal could leave Kabul ill-equipped to keep the Taliban at bay and extremist elements out, Obama vowed not to let Afghanistan again become a "safe haven" for terrorists.

He touted the recent death of bin Laden as a "victory for all who have served since 9/11," and he claimed intelligence recovered from the terror leader's Pakistan compound revealed that Al Qaeda is under "enormous strain." Obama said bin Laden had expressed concern that Al Qaeda could not replace senior leaders who were killed and was struggling "to portray America as a nation at war with Islam."

Senior administration officials said the president reached his withdrawal decision after reviewing the "substantial progress" made toward three goals: denying Al Qaeda a safe haven in Afghanistan, reversing the Taliban's momentum so they cannot topple the government and training Afghan security forces.

One official noted that for the past six years or more, the terrorist threat has come from Pakistan and not Afghanistan. "We don't see a transnational threat coming out of Afghanistan," the official said, claiming the pullout would not affect counterterror operations in Pakistan.

Officials said the U.S. at the same time is supporting Afghan efforts to reach a "political settlement" with some parts of the Taliban, acknowledging that the goal is not to eradicate the Taliban entirely.

Obama briefly spoke about those talks Wednesday night, saying the administration believes "progress can be made." He said the talks must be led by the Afghan government, and Taliban members who want to integrate must "break from Al Qaeda, abandon violence and abide by the Afghan Constitution."

But as the president tried to appeal to hawks and doves alike on Afghanistan, some in both camps were left unhappy.

Anti-war Rep. Barbara Lee, D-Calif., scoffed at the president's announcement, saying such a reduction in 2011 would "not even get us back to pre-escalation levels." She suggested withdrawing 50,000 combat troops and is planning several amendments aimed at de-funding the mission.

House Democratic Leader Nancy Pelosi also said in a statement after the speech that many in Congress hoped the "full drawdown of U.S. forces would happen sooner than the president laid out -- and we will continue to press for a better outcome."

Critics of the war are surely bolstered by polling that shows Americans increasingly opposed to the U.S. presence in Afghanistan. A Pew Research Center survey showed that for the first time a majority of those polled -- 56 percent -- says troops should be withdrawn as soon as possible. A majority also believes the U.S. will probably succeed in Afghanistan.

Democrats have been joined by Republicans, some Tea Party-aligned, in calling for a swift end to the war. Even some GOP candidates for president have echoed the call.

But as the president faces bipartisan pressure to get out of Afghanistan, he also faces bipartisan pressure not to leave too quickly.

Rep. Mike Rogers, R-Mich., chairman of the House Intelligence Committee, expressed concern that the withdrawal plan would put too much of a burden on the remaining troops and "increase risk in a number of areas."

House Speaker John Boehner said Wednesday he'd be "concerned about any precipitous withdrawal" from Afghanistan.

"We all want to bring our troops home as quickly as possible, but we must ensure that the gains we've made are not jeopardized," Boehner said after the speech, urging the president to take into account the advice of commanders on the ground.

Sen. Bill Nelson, D-Fla., in a YouTube video cut before the president's speech, said Obama has "the right idea about starting a withdrawal" without allowing "the terrorists to gain safe haven elsewhere in the region."

The president's speech Wednesday only marked the start of discussion on Capitol Hill about his withdrawal strategy. The House Armed Services Committee is planning a hearing Thursday. Chairman of the Joint Chiefs of Staff Adm. Mike Mullen is slated to testify.

Fox News has also learned House Democratic leaders plan to meet with Obama at the White House on Thursday. Though the discussion will focus on the status of debt-ceiling talks, a source familiar with the talks suggested Afghanistan, as well as Libya, could come up.