WASHINGTON — Fighting a swell of economic anxiety, President Barack Obama has lost much of the narrow lead he held just a month ago over Mitt Romney and the two now are locked in a virtually even race for the White House, according to a new Associated Press-GfK poll. The survey also found a majority of Americans disapproving of how the Democratic president is handling a national economy that fewer people think is improving.

Less than five months before the election, 47 percent say they will vote for the president and 44 percent for Romney, a difference that is not statistically significant. The poll also shows that Romney has recovered from a bruising Republican primary.

The economy remains Obama’s top liability. Only 3 out of 10 adults say the country is headed in the right direction and 55 percent disapprove of his handling of the economy, the highest level detected in AP-GfK polls this year.

“I’m not going to vote for Obama,” said Raymond Back, a 60-year-old manufacturing plant manager from North Olmsted, Ohio, one of the most competitive states in this election. “It’s just the wrong thing to do. I don’t know what Romney is going to do, but this isn’t the right way.”

Yet, in a measure of Romney’s own vulnerabilities, even some voters who say they support Romney believe the president will still be re-elected. Of all adults polled, 56 percent believe Obama will win a second term. And despite three months of declining job creation that have left the public increasingly glum, Romney has not managed to seize the economic issue from the president, with registered voters split virtually evenly on whether Romney or Obama would do a better job improving it.

The polling numbers come as no surprise to either camp. Both Romney and Obama advisers have anticipated a close contest that will be driven largely by economic conditions. The Obama camp is busy trying to define Romney, hoping it is reaching more independents like Doss Comer, 58, of Jacksonville, N.C., who said he would vote for Obama again, despite the lagging economy.

“I think we are on the wrong track,” he said. “We’re not getting anywhere. We’re not growing. The unemployment rate just spiked up again.” But, he added: “I don’t trust Romney because of what he’s doing. He’s telling his business experience, that he was an investor in business. ... I don’t think he has the right background any more than Obama.”

Over time, polls that measure Obama’s standing have reflected fluctuations in the economy, which has shown both strength and weakness since it began to recover from the recent recession. The new survey illustrates how an ideologically divided country and a stumbling recovery have driven the two men into a tight match.