(Corrects fourth paragraph to show drillers added one rig in Granite Wash, deletes reference to four basins)
By Scott DiSavino
June 12 (Reuters) - The market has been waiting for the slowdown in the rig count to stop as crude prices have rebounded over the past few months, but this week's slowdown showed oil drillers were not yet done cutting the number of rigs.
Energy firms pulled another seven rigs from U.S. oil fields this week, the most since late May, oil services company Baker Hughes Inc said on Friday in its closely followed report.
That was the 27th straight weekly decline, bringing the total rig count down to 635, the lowest since August 2010.
Drillers this week added a rig in just one basin, the Granite Wash located in the Texas Panhandle and Oklahoma.
With Saudi Arabia and Iraq pumping oil at record or near record levels, the Organization of the Petroleum Exporting Countries last week kept its output target at 30 million barrels per day as it tries to keep crude prices low to support global oil demand growth while retaining market share by driving out more expensive producers, like U.S. shale drillers.
That OPEC policy has worked, as world oil demand is picking up and supply has slowed.
U.S. drillers have eliminated thousands of jobs and idled more than half of the country's active rigs since they peaked at 1,609 in October as U.S. crude futures collapsed 60 percent from over $107 a barrel last June to a six-year low near $42 in March on oversupply concerns.
But with U.S. crude prices averaging around $60 since the start of May, U.S. energy companies have started to return to drilling in some of the biggest shale fields.
JBC Energy, an energy research and consulting firm, said the Eagle Ford in South Texas was experiencing a slow recovery in new drilling activity, while the idling of rigs in the Permian in West Texas and eastern New Mexico seems to be bottoming out.
The Permian is the biggest U.S. shale oil basin and the Eagle Ford is the second biggest.
Last week, U.S. crude production climbed to over 9.6 million barrels a day, its highest level since the early 1970s, according to government data.
"It seems the intense focus on rig counts has slacked off a bit during recent weeks as it is increasingly confirmed the significant decline in U.S. upstream activity is not having a dramatic impact on supply in the short term," analysts at JBC Energy said. (Reporting by Scott DiSavino; Editing by Meredith Mazzilli)