Declines in U.S. manufacturing activity slowed last month, raising the likelihood that the sector — and perhaps the broader economy — could see growth in the second half of the year. But separate reports showed the labor market remains weak, an obstacle to recovery.

Rising production and a shallower drop in employment helped push the Institute for Supply Management’s index of manufacturing activity to 44.8 in June from 42.8 in May. It was the sixth straight monthly increase, though activity still remains below the 50 level that signals overall growth in the sector.

“The sector is a relatively small part of overall U.S. employment and gross domestic product, but it serves as a useful business barometer. Though activity is improving, prospects for a swift recovery are shaky: A key gauge of production — new orders — declined in June following three monthly gains.

Separately, a June employment report from payroll company Automatic Data Processing Inc. showed a continuing weak labor market. ADP said the U.S. shed 473,000 private-sector jobs last month — the smallest decline since October, but a higher number than expected and a sign that the government’s official estimate, released Thursday, could show little improvement.

Meanwhile, the U.S. housing market continues to show tentative signs of recovery.

Pending home sales, an index of contracts signed that is typically released about a month before reported sales, rose slightly in May, the National Association of Realtors said. The index gained 0.1 point to a seasonally adjusted 90.7, its highest level since September. Pending sales rose in the Northeast and West, and dipped in the Midwest and South. An index level of 100 represents contract activity in 2001, the first year the data were collected.

Also Wednesday, the Commerce Department said spending on construction nationwide declined in May, falling 0.9% to $964 billion at a seasonally adjusted annual rate. The drop was led by a 3.5% decline in residential construction spending to $247.4 billion. While residential spending levels are down a third from a year ago, the declines from April through June are shallower than in the first quarter, which economists say should help buoy second-quarter GDP.

Spending on nonresidential construction, meanwhile, held steady in May, rising 0.1% to $716.7 billion, and stayed slightly below year-ago levels. Spending on education, health care and manufacturing rose from April to May, while lodging, offices and roads spending declined.

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