WASHINGTON — U.S. builders started work on more single-family homes in May and requested the most permits to build homes and apartments in three and a half years. The increase suggests the housing market is slowly recovering even as other areas of the economy have weakened.

The Commerce Department said Tuesday that builders broke ground on 3.2 percent more single-family homes in May, the third straight monthly increase.

Overall housing starts fell 4.8 percent last month to a seasonally adjusted annual rate of 708,000. But that was entirely because of a 21.3 percent plunge in apartment construction, which can be volatile from month to month.

The government also said April was much better for housing starts than first thought. The government revised the April starts to 744,000 – up from an initially reported 717,000 and the fastest building pace since October 2008.

And builders are more optimistic about the next 12 months. They requested more permits to build homes, a gauge of future construction. Permits increased to a seasonally adjusted rate of 780,000 – the most since September 2008.

Even with the gains, the rate of construction and the level of permits requested remain roughly half the pace considered healthy. Yet the increases add to other signs that the home market may finally be starting to recover nearly five years after the housing bubble burst.

The mostly positive report contributed to a strong opening on Wall Street, although much of the rally was driven by expectations that the Federal Reserve will take action this week to jumpstart the economy.

Many economists believe that housing construction could contribute to overall economic growth this year for the first time since 2005.

“We continue to expect housing activity to increase gradually in coming months and residential investment to make a positive contribution to GDP growth,” said Peter Newland of Barclays

By region of the country, housing starts rose 14.4 percent in the West, but dropped in other parts of the country.Economists say it could be years before the market is fully healed.

Many people are still having difficulty qualifying for home loans or can’t afford larger down payments required by banks.

Though new homes represent just 20 percent of the overall home market, they have an outsize impact on the economy. Each home built creates an average of three jobs for a year and generates about $90,000 in taxes, according to data from the Home Builders.