A former top economic adviser to President Obama now says he regrets not doing more to help the unemployed during the worst years of the recession.

Alan Krueger, who was an assistant secretary of the Treasury from 2009 to 2010 and later served as chairman of the president’s Council of Economic Advisers, said Wednesday that he worries many of the long-term unemployed will never work again — and that he wishes the administration had done more to help them before it was too late.

“I regret that we didn’t do more to help the short-term unemployed avoid falling into long-term unemployment,” Mr. Krueger wrote in an email.

Krueger, who now teaches economics at Princeton University, on Thursday will present a new paper on the plight of people out of work for more than six months. The findings are bleak: Krueger and his two co-authors found that few of these long-term unemployed get a job, and fewer still gain steady jobs. Worse, there’s little sign their odds are improving as the economy recovers.

Economists have long known that the longer someone remains unemployed, the less likely she is to find a job. But there’s much less agreement on whether the long-term jobless have become permanently unemployable, or whether they will return to work when the economy improves.

Krueger and his coauthors, Princeton economists Judd Cramer and David Cho, find evidence that the long-term unemployed aren’t getting jobs even in parts of the country where the job market is comparatively healthy, suggesting that a stronger economic rebound won’t be enough to put them back to work.

“An improving economy will help, but it’s not enough,” Krueger said. “Given the scale of the problem, it’s not going to be sufficient.”

Krueger said the severity of the recession meant there may have been little anyone could do to prevent the unprecedented levels of long-term unemployment the U.S. has experienced in recent years. He criticized Congress for not passing more of the Obama administration’s job proposals in 2010 and 2011, and the Federal Reserve for ending its initial round of stimulus too soon. And he said he regretted not finding a way for the government to keep employing some of the hundreds of thousands of people hired to carry out the 2010 Census.

“The lesson I take away is: Try to prevent the short-term unemployed from becoming long-term unemployed,” he said.