WASHINGTON — The job market is looking up, according to a report on the U.S. private sector released yesterday, and a separate analysis by the Treasury Department's top economist.

Companies in the U.S. private sector added 32,000 jobs in April, according to the ADP employment report released yesterday.

The report, coming two days before the Labor Department reports on changes in the nation's nonfarm payrolls for April, added to the sense that there would be a sizable increase in jobs.

Economists are expecting a 185,000 increase in nonfarm payrolls. It would be the biggest gain in three years.

In testimony to the Joint Economic Committee of Congress later on Wednesday, Alan Krueger, the assistant Treasury secretary for economic policy, said the labor market is beginning to show signs of "sustained improvement."

Krueger said new data show that employment at large firms has increased in five of the past six months — "a possible early sign of durable job growth."

The unemployment rate, however, could be hard to bring down for a while.

The economists in the MarketWatch survey ahead of Friday's report, on average, predict the unemployment rate will stay at 9.7 percent for the fourth straight month in April.

Labor demand at small firms has continued to be weak, Treasury's Krueger said.

Krueger said it was too soon to know whether the unemployment rate peaked at 10.1 percent last October.

The unemployment rate could retest the cyclical high if workers who have dropped out of the labor force flood back in.

As a rough guess, about 3.5 million Americans dropped out of the labor force during the recession, and many of those will compete for jobs with the 15 million who are officially classified as unemployed.

The increase in ADP employment was close to the consensus forecast of economists surveyed by MarketWatch in which they had called for an increase of 35,000.

ADP said there have been job gains over the past three months as a result of an upward revision for March. March job gains rose a revised 19,000 up from the initial estimate of a decline of 23,000.

Joel Prakken, chairman of Macroeconomic Advisers LLC that prepares the report, described the increases, averaging 18,000 over the past three months, as "grudging."

The ADP report does not include federal workers or temporary census workers.

Payrolls are expected to expand in April and May with the Census hiring temporary workers it needs to complete the door-to-door canvass of those who didn't return their forms by mail.

Employment in the service-providing sector in April rose by 50,000, and employment in factories rose 29,000.