“I think at this point the U.S. economy has a very good chance of being able to continue its recovery despite the uncertainty in Europe,” said Bernard Baumohl, chief global economist at the Economic Outlook Group. “But the threat is real, and we have to be vigilant and very nimble.”

President Obama called April’s job report “particularly heartening.” He noted that “this week’s job numbers come as a relief to Americans who’ve found a job, but it offers, obviously, little comfort to those who are still out of work.”

All manner of businesses were hiring, including those in manufacturing, leisure and hospitality and health care. One of the strongest gains occurred in manufacturing, which added 44,000 jobs, the largest increase since 1998.

The Census Bureau contributed 66,000 temporary jobs last month.

Yet, in a sign that many people will struggle to find a job even as the economy improves, the number of people who have been out of work for more than six months hit 6.7 million, nearly 46 percent of the unemployed. “The economic recovery and expansion is entrenched, sustained and sustainable,” Allen L. Sinai, chief global economist at Decision Economics, said. But he warned that the economy faced numerous challenges, including the need for the United States to deal with its own domestic debt and a possible downturn in exports to Europe.

“It’s like having symptoms of a heart attack,” Mr. Sinai said, “either you ignore them or take preventive action to make sure there will be no heart attack.”

The increase in April was accompanied by a revised gain for March of 230,000 jobs, up from 162,000. While the levels of the last two months exceeded the 150,000 jobs a month that many economists say is necessary to accommodate new entrants to the job market, they were still not nearly as high as the average after previous recessions.

Image Census employees after a training course in New York last month. Credit... Bebeto Matthews/Associated Press

The number of unemployed people actually rose slightly from March, to 15.3 million. And the so-called underemployment rate — which includes people whose hours have been cut as well as those working part time because they cannot find full-time jobs — rose to 17.1 percent, from 16.9 percent in March.