Stephen Crowley/The New York Times

At the height of the Iraq war in 2004, veterans gave President George W. Bush a 16-percentage-point edge over his Democratic rival. Four years later, Barack Obama trailed among the former military members by 10 percentage points.

But Mr. Obama’s campaign said it thinks his three and a half years as commander in chief have turned the tables on the issue, giving him a good chance at winning the veteran vote this year.

One of Mr. Obama’s first campaign ads — released just this week — was aimed directly at war-weary service members and their families.

“It’s because of what they’ve done that we’ve been able to go after al-Qaeda and kill Bin Laden,” Mr. Obama says in the ad. “And when they come home we have a sacred trust to make sure that we are doing everything we can to heal all of their wounds, giving them the opportunities that they deserve to find a job and get the education that they need.”

The ad is part of Mr. Obama’s efforts to capitalize on a very different profile than is typical for a Democratic president.

Having come into the White House on an antiwar platform, Mr. Obama nonetheless increased American involvement in Afghanistan even as he began drawing down troops in Iraq. Now, both wars are winding down — a

relief to many military members and their families.

In addition, Mr. Obama has embraced the use of drones to assassinate terrorist leaders. And he authorized the raid that led to the killing of Osama bin Laden.

“President Obama is committed to ensuring that all of our men and women who’ve served in uniform can find work when they return home, receive the health care and benefits they’ve earned and have the chance to get a college education through the post-9/11 G.I. Bill,” said Clo Ewing, a campaign spokeswoman.

Working in Mr. Obama’s favor may be the changing face of the American military, which is becoming younger and more diverse. Advisers to the president note that he actually won in 2008 among veterans who were under 60 years old.

The military is also changing in its attitudes toward social issues, the Obama campaign believes. Mr. Obama’s decision to end the “don’t ask, don’t tell” ban on gays serving openly will be a benefit, they say.

There is little recent polling to suggest how the two candidates are faring among veterans. But advisers to Mr. Romney scoff at the idea that Mr. Obama will steal away a traditional Republican advantage come Election Day. They argue that the president’s economic policies have been especially detrimental to veterans and their families.

“The president’s policies have not provided opportunity for the next generation of soldiers who are returning home from the battlefield,” said Ryan Williams, a spokesman for Mr. Romney. “We think that’s an important distinction.”

Mr. Williams said unemployment among veterans of the Iraq war stands at 9.2 percent, higher than the 8.1 percent rate for the nation as a whole. And, he said, nearly one in five veterans of that war was unemployed in April.

“President Obama’s policies have failed veterans and they are looking to elect a different president,” Mr. Williams said.

Both campaigns lay claim to having the better ideas for helping veterans once they come home.

Mr. Obama’s campaign points to the Post-9/11 G.I. Bill that the president signed into law as evidence of how his policies have already helped veterans. Mr. Romney’s campaign says Mr. Obama’s budget cuts veterans benefits deeply.

But the effort to woo military members and their families also depends on the candidates’ broader approach to military issues and waging war — and on how to pay for it.

Mr. Romney’s campaign is using the president’s support of the debt-ceiling deal last year that would force huge cuts in defense spending if Congress can’t find a way to avoid them. Mr. Romney has opposed the defense cuts, calling them a danger to the quality of the armed forces.

Mr. Williams, the spokesman for Mr. Romney, called them “devastating and crippling defense cuts” that would “leave our armed forces in a state of disarray. These irresponsible defense cuts do not appeal to veterans.”

Campaign aides to the president counter that Mr. Romney’s proposals would leave veterans without the proper care and respect the deserve. Ms. Ewing said Mr. Romney ”suggested privatizing veterans’ health care, eliminating the department that helps homeless veterans and fails to mention veterans once in his 160-page, 59-point plan for jobs and economic growth.”

Mr. Obama’s advisers are also betting that the public at large — and veterans in particular — will not view the president as weak on defense, in part because of the actions he’s taken as president.

The ad his campaign released this week features grainy, green-tinted video of military operations on the screen as Mr. Obama praises the soldiers who went on the raid that killed Bin Laden.

Mr. Obama also frequently mentions the Bin Laden raid in speeches and on the campaign trail. During a commencement speech to members of the Air Force Academy this week, Mr. Obama said that “for the first time

in your lives — and thanks to Air Force personnel who did their part — Osama bin Laden is no longer a threat to our country.”

Advisers in Chicago, where Mr. Obama’s campaign has its headquarters, are also counting on support from veterans who are happy that the wars in Afghanistan and Iraq are coming to an end. Many soldiers and Marines served multiple tours of duty in those countries.

In the end, though, it remains an open question whether Mr. Obama’s actions as president — and a changing military — can help him overcome the traditional advantage that Republicans have held among veterans.

The answer to that question may not come until Election Day.