(Adds basin details, natural gas rigs in paragraphs 9-11)
Nov 6 (Reuters) - U.S. energy firms cut oil rigs for a tenth week in a row this week, decreasing the pace of decline from recent weeks, data showed on Friday, a sign low prices continued to keep drillers away from the well pad.
Drillers removed six oil rigs in the week ended Nov. 6, bringing the total rig count down to 572, the least since June 2010, oil services company Baker Hughes Inc said in its closely followed report.
That is around a third of the 1,568 oil rigs operating in same week a year ago. Over the 10 weeks, drillers cut 103 oil rigs.
Although U.S. oil futures have averaged $46 a barrel so far this week, up from $45 last week, the front-month December contract was on track to post its third weekly decline in four as an oversupply of physical oil and a strong dollar bedeviled the market.
Energy traders noted the rate of oil rig reductions over the past two months - about 11 on average - was much lower than the 19 rigs cut on average over the past year since the number of rigs peaked at 1,609 in October 2014, due in part to expectations of slightly higher prices in the future.
U.S. crude futures for next year were trading around on average almost $49 a barrel, according to the full year 2016 calendar strip on the New York Mercantile Exchange.
Higher prices encourage drillers to add rigs. The most recent time crude prices were much higher than now was in May and June when U.S. futures averaged $60 a barrel.
In response to those higher prices, drillers added 47 rigs over the summer.
Despite the overall oil rig count reduction, drillers added rigs in three of the four major U.S. shale oil basins this week. They added four in the Permian in West Texas and eastern New Mexico, and one each in the Bakken in North Dakota and Montana and the Niobrara in Colorado and Wyoming, while cutting three in Eagle Ford in South Texas.
With the latest cuts the total number of oil rigs in the Eagle Ford fell to the lowest level since 2011.
With the decline in oil rigs this week, total oil and gas rig count slid to a fresh 13-year low despite an increase of two gas rigs.
Reporting by Scott DiSavino; Editing by Marguerita Choy