The national unemployment rate fell to its lowest level in more than four years in April, according to data released Friday, sending stock markets to new heights and dispelling fears that the recovery had stumbled.

Businesses hired more people than analysts expected, pushing the jobless rate down to 7.5 percent from 7.6 percent in March. The Labor Department reported that the economy in April added 165,000 jobs across a broad swath of industries. Just as importantly, the agency significantly increased its estimates of job growth for the previous two months. The average monthly gain this year is now just shy of 200,000 — the minimum pace required to ensure the recovery can lift off.

Stock markets surged on the good news. Both the Dow Jones industrial average and the broader Standard & Poor’s 500-stock index crossed into record territory Friday morning. Markets have already broken several records this year, helping to rebuild household wealth and retirement portfolios.

However, there were weak spots in Friday’s data: The public sector continued to shrink, and the average work week declined slightly. But the reading overall was solid and should alleviate concerns that the economy was once again stuck in the mud, dragged down by higher taxes and deep government spending cuts.

“There is nothing inevitable about the U.S. recovery yet, but its momentum is building, and equities are buoyant,” said Viktor Nossek, head of research at securities trading firm Boost ETP.

The economy’s strength is coming from the private sector. Professional and business services led the way in April, adding 73,000 jobs. Restaurants and bars accounted for 38,000 positions, while retailers gained 29,000. Growth in those sectors suggests that American consumers — the engine of the nation’s economy — are becoming more willing to open up their wallets despite higher taxes.

The federal government’s financial cutbacks, however, are still weighing on the labor market. April marked the second month of the across-the-board federal spending cuts known as the sequester. The federal government shed about 8,000 jobs last month, according to Friday’s data, while state and local governments shaved off another 3,000.

Paul Edelstein, U.S. economist for IHS Global Insight, said the impact of the sequester will also likely show up in the length of the average work week, as many employees could be furloughed rather than fired. He expects the sequester to shave about 0.4 percent from economic growth this year.

In a statement, the Obama administration said it is pushing for spending on infrastructure to boost job growth. The White House also noted that the economy consistently has added jobs for more than three years.

“While more work remains to be done, today’s employment report provides further evidence that the U.S. economy is continuing to recover,” wrote Alan Krueger, chairman of the Council of Economic Advisers.