By Eric Morath

The Labor Department is struggling to document accurately how many workers are unemployed in the recession caused by the coronavirus pandemic, a difficulty the government has faced during other times of rapidly changing economic conditions.

A "misclassification error" caused the overall unemployment rate to be lower than it would have been otherwise, the department said in the May jobs report, released last week. It was the third straight month the department issued such a warning.

While the figures may differ, the error doesn't change the broader story told by the unemployment data: the number of Americans without jobs remains historically high, and signs of a labor-market recovery emerged in May as payrolls rose and the unemployment rate, however it is calculated, fell from the prior month.

The unemployment rate was 13.3% in May but would have been 16.3% without a misclassification related to responses that workers gave when asked about their employment status, the Labor Department said in a special note in the report. The April rate of 14.7% would have been 19.7%, the Labor Department said. March's rate would have also been higher.

The misclassification, according to the department, occurred because many respondents to the survey of households that determine the unemployment rate reported themselves as "employed but absent from work." Such a classification in a more normal time could include those on vacation. The department said in the last three jobs reports that it believes many people falling in that category in recent months should be counted as unemployed.

Those who worked zero hours because of the coronavirus pandemic during the period of a survey should have been counted as unemployed, according to the Labor Department, even if they were paid or received some other form of compensation from their employers.

The Bureau of Labor Statistics, the department's statistical arm, recognized the possibility of the misclassification occurring in March, when the pandemic's effect on the economy was becoming clear, said Associate Commissioner for Employment and Unemployment Statistics Julie Hatch Maxfield in an interview. The BLS flagged the situation to U.S. Census Bureau interviewers and in subsequent months provided additional training, including holding conference calls.

Because the error has continued to occur, interviewers in June will be reminded of proper classification protocol directly in the software where they record survey results, she said.

While the BLS has recognized the misclassification, it has maintained its usual practice of not reassigning survey responses.

Some people have raised the prospect that the figures are being manipulated by the Trump administration, an idea that has gained traction on social media.

Ms. Maxfield, who started at the bureau in 1999, said the bureau's mission of accuracy and transparency doesn't change by administration or economic situation.

"It's not like someone else discovered this," she said. "We put it in our news release, in a box, that says you should pay special attention to this. And we released several pages of additional documents."

Economists appointed by presidents from both parties say there is no sign the data were manipulated. Instead, they said that data are most difficult to accurately collect and report during times of extreme change and that the job displacement caused by the pandemic is without modern precedent.

"I appreciate the fact they're being so transparent about this," said Katharine Abraham, who led the BLS after President Clinton appointed her. She later served as an economic adviser to President Obama. "The problem is this is a novel situation for a data collector -- in a normal time you wouldn't run into anything that would look like this," she said.

Keith Hall, who led the BLS under President George W. Bush during the financial crisis, said he sympathizes with how difficult it is to report the figures in times of rapid change. Labor Department officials have "been really transparent and haven't changed their methodology -- and that's the exact right thing to do," he said.

Mr. Hall said he testified in Congress in late 2008 after the bureau reported a historically bad jobs report, showing hundreds of thousands of Americans had lost their jobs. "I had to tell members of Congress, when you remove seasonal adjustments that smooth the data, the jobs loss was more than reported," he said.

The 42-page-long jobs report for May has thousands of figures giving details on the labor market beyond the closely watched unemployment rate.

The Labor Department produces several alternative measures of labor underutilization, besides the official unemployment rate. One of those, known as the U-6, counts those who are outside the labor market but who looked for a job in the past year, and those who work part time but want full-time work.

That measure rose to 22.8% in April, the highest in records going back to 1994. In May, the U-6 fell to 21.2%.

Aggregate hours worked in the private sector, a separate reading in the report, is another measure of the state of the job market. It reflects those who had hours cut or were told not to report to jobs but remained on payrolls. That measure fell about 15% in April and rose more than 4% in May.

"It's a mistake to get too focused on the unemployment rate as the one number that tells the story," Mr. Hall said. "It's a lot more complicated than that."

Write to Eric Morath at eric.morath@wsj.com