The U.S. oil-rig count rose for the third straight week—this time by six to 670—in the latest week, according to Baker Hughes Inc. BHI -1.49 %

The number of U.S. oil-drilling rigs, which is a proxy for activity in the oil industry, had fallen sharply since oil prices headed south last year. The rig count had dropped for 29 straight weeks before rising for two weeks, falling, then rising again.

Oil prices fell nearly 60% from June 2014 to a six-year low in March, as soaring production from the U.S. and other countries overwhelmed global demand.

There are still about 58% fewer rigs working since a peak of 1,609 in October, though the pace of declines has slowed considerably recently. In late May, several U.S. shale-oil companies said they were ready to bring rigs back into service, setting up the first big test of their ability to quickly react to rising crude prices.

According to Baker Hughes, gas rigs were up by four to 213 this week.

The U.S. offshore rig count was up four to 38 in the latest week, though it is still off 24 from a year earlier.

For all rigs, including natural gas, the week’s total was up 10 to 884, which is down 1,024 rigs from the same period last year.

Write to Angela Chen at angela.chen@wsj.com

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