NEW YORK (AP) — President Obama’s approval ratings are starting to rise after declining ever since his inauguration, new poll figures show as the country’s mood begins to brighten. But concerns about the economy, health care and war persist, and support for the war in Afghanistan is falling.

An Associated Press-GfK poll says 56 percent of those surveyed in the past week approve of Obama’s job performance, up from 50 percent in September. It’s the first time since he took office in January that his rating has gone up.

People also feel better about his handling of the economy and his proposed health care overhaul.

But not about the war.

Support for the war in Afghanistan has declined, the poll said Tuesday. And approval of Obama’s handling of it is holding steady — in contrast to his gains in other areas — as he considers a big troop increase there. Poll respondents narrowly oppose the increase.

Overall, 39 percent said they disapproved of Obama’s performance in office, down from 49 percent last month.

While a majority of those surveyed remain pessimistic about the direction of the country, that number has begun to improve, too. The poll found 41 percent now believe the U.S. is headed in the right direction, compared with 37 percent in September.

But a large majority of respondents said they remain very concerned about most of the major issues facing the country. The economy was the biggest concern, with 88 percent saying they consider it extremely or very important, followed by unemployment, health care, terrorism, the budget deficit, taxes and the war in Afghanistan.

The increase in Obama’s job approval rating was driven by a more positive view of his handling of nearly all of those issues.

Fifty percent of those surveyed said they approved of the president’s handling of the economy, up from 44 percent in September.

And 48 percent said they approved of his handling of health care, up six points.

and about equal to the 47 percent who said they disapproved. Obama has made health care the signature domestic issue of his presidency.

Terence Glass, a 45-year-old Milwaukee resident studying to be a teacher, said he was pleased with Obama’s handling of health care and the economy, especially his decision to provide federal help to the ailing auto industry.

‘‘We have to look at what was going on before he got in his office. The country was in pretty bad shape,’’ Glass, a Democrat said, adding that since Obama had become president, ‘‘I look at it now and I think it’s doing a little better.’’

The only measure that remained unchanged from September was Obama’s handling of the war in Afghanistan. Forty-six percent said they approved of his handling of the conflict, while 41 percent disapproved.

Indeed, the poll found a drop in overall support for the 8-year-old war. Forty percent said they favored it, down four points from July, while 57 percent said they were opposed. Some 46 percent favor sending more U.S. troops there, while 50 percent oppose a troop increase, a major decision Obama is weighing.

Obama boosted troop levels in Afghanistan last spring by about 21,000. He and his national security team are now reviewing a warning by Gen. Stanley McChrystal, commander of U.S. forces in that country, that the war will be lost without another big increase.

Glenda Holton, 53, a retired Army sergeant from Dublin, Ga., said she strongly disapproved of Obama’s performance in office — and opposed a troop increase.

‘‘I don’t feel like they need to have any of them over there,’’ she said about U.S. troops in Afghanistan. ‘‘Because it’s not doing any good, it’s escalating and there hasn’t been any improvement.’’

Holton, who did not vote for Obama in the general election and considers herself an independent, added, ‘‘It’s not our fight over there.’’

To be sure, the poll found persistent and deep partisan divisions over Obama. While 88 percent of Democrats said they approved of his performance in office, just 18 percent of Republicans approved. But that GOP figure was up six points since September, when only 12 percent of Republicans said they approved.

Obama’s job approval has also gone up among independents. Fifty-three percent said they approved of the president’s job performance, a nine point increase since September. Even more strikingly, the percentage of independents who said they disapproved plunged 16 points, from 53 percent last month to 37 percent now.

The poll of 1,003 adults was conducted Oct. 1-5, using both landline and cell phone interviews, with a margin of sampling error of plus or minus 3.1 percentage points.