Afghan national police officers and U.S. Marines rush with a badly wounded Afghan police officer to a medevac helicopter in the Helmand province of southern Afghanistan, June 3, 2011. (Anja Niedringhaus/AP)

The number of Americans who say the war in Afghanistan is worth fighting has increased for the first time since President Obama announced at the end of 2009 that he would boost troop levels, according to a new Washington Post-ABC News poll.

The finding may give Obama slightly more political breathing room as he decides how many troops to withdraw from Afghanistan in July, the deadline he set 18 months ago to begin bringing home the additional U.S. forces.

In the Post-ABC News poll conducted last week, 43 percent of Americans say the war is worth fighting, compared with 31 percent in March. A significant amount of the fresh support came from the independent voters Obama is courting as he campaigns for reelection next year.

But a majority of Americans still say the war, which is in its 10th year, is not worth fighting, despite the killing last month of Osama bin Laden by U.S. forces in Pakistan.

The 16-point bump in support that Obama received for his handling of the war immediately after bin Laden’s death has been cut in half, the poll found.

In addition, nearly three in four Americans say the administration should remove a “substantial number” of troops from Afghanistan this summer, although fewer than half of those polled think the government will do so.

The findings frame the national debate as Obama, who met Monday with his national security team to discuss Afghanistan, nears a decision on how many of the roughly 100,000 U.S. troops to withdraw next month.

He is doing so amid an increase in U.S. combat deaths in Afghanistan that has coincided with the start of the spring fighting season. Seventy six American service members were killed in Afghanistan in April and May; 54 combat deaths were recorded over the same two months the previous year.

Obama has said that the initial troop withdrawal will be “significant,” with estimates in the 3,000 to 5,000 range. Bin Laden’s death has given new impetus to those within the administration, primarily Obama’s civilian advisers, who favor a more aggressive drawdown than some military officers. He will probably have several options from which to choose.

“It’s rare that only one alternative would be on the table,” Jay Carney, Obama’s press secretary, told reporters Monday, adding that the president will decide on a number “relatively soon” even though he has not received a recommendation from his combat commanders.

But some administration officials say more important than the first withdrawal is setting the deadline for when all 30,000 troops that Obama deployed to Afghanistan at the end of 2009 will be brought home.

Several senior administration officials would like all those forces withdrawn by the end of the year, allowing Obama to tell his skeptical Democratic base in an election year that he is winding down the war. To date, he has relied largely on Republican support in Congress to execute his Afghanistan policy.

But Defense Secretary Robert M. Gates came out Monday against a swift shift to a smaller counterterrorism-focused mission, telling troops in Afghanistan that the United States should keep the military pressure high throughout the year to force the Taliban to negotiate.

On the third day of a trip to Afghanistan, his last visit to the war zone as defense secretary, Gates praised the military progress against the Taliban and al-Qaeda but said, “We’ve still got a ways to go, and I think we shouldn’t let up on the gas too much, at least for the next few months.”

“If we keep the military pressure on through this winter, and we are able to hang on to what we’ve taken away from these guys over the last year to 18 months . . . then it may be that some time around the end of this year these guys decide, ‘Maybe we ought to start talking seriously about reconciliation,’ ” Gates said at Combat Outpost Andar in the Ghazni province of eastern Afghanistan. “That certainly is my hope.”

The new Post-ABC News poll found that opposition to the war within the Democratic Party fell from 79 percent in March to 63 percent.

Obama is also enjoying more support for his war policy from independent voters. In March, just over a quarter of independents said the war was worth fighting. That number jumped to 45 percent in the most recent poll.

The telephone poll was conducted this past Thursday to Sunday, among a random national sample of 1,002 adults. The results from the full survey have a margin of sampling error of plus or minus 3.5 percentage points.

Correspondent Josh Partlow at Combat Outpost Andar, Afghanistan, and staff writer Rajiv Chandrasekaran and staff researcher Julie Tate in Washington contributed to this report.