Total U.S. crude oil production reached 9.6 million barrels per day, with output from the Lower 48 states showing some recovery, federal data show.

The total U.S. crude oil production for the week ending June 5 was about a quarter of a percent higher than the previous week. The U.S. Energy Information Administration reports 9.1 million bpd came from the Lower 48 and 509,000 bpd came from Alaska, which in the EIA's last report was the lone standout in production gains.

Though Alaska is the No. 4 oil producer in the nation, its production is in decline as many state reserve areas reach maturation.

The low price of crude oil has left energy companies with less cash for exploration and production. The trend may be reversing, however, as crude oil rallies above the sub-$50 per barrel climate of early 2015.

West Texas Intermediate, the U.S. benchmark, is up more than 2 percent from last week to around $60 per barrel.

In its latest monthly market report, the Organization of Petroleum Exporting Countries said crude oil prices may be at or near their ceiling for the year.

EIA said in a drilling productivity report from early this week that oil production from some of the more lucrative shale basins in the United States is expected to drop by a combined 92,000 barrels per day by July. While the Eagle Ford shale play in Texas is expected to show the largest drop in terms of volume, the Niobrara shale in Colorado declines the most in terms of percent by July, federal data show.

Nevertheless, an annual statistical review from BP this week found U.S. oil and production has put it in the lead in terms of global output.