U.S. crude oil production increased slightly for the week ending Jan. 2 despite a decline in rig activity and slumping prices, government data show.

The U.S. Energy Information Administration said in a weekly petroleum status report total U.S. oil production was 9.13 million barrels per day for the week ending Jan. 2, up about 11,000 bpd from the previous week.

Production from the Lower 48 was behind the entire gain as output from Alaska was unchanged from the previous week.

Oil prices are at the point where some companies working in U.S. shale basins and elsewhere in North America are cutting back on spending programs. Oil services company Baker Hughes in its latest assessment of the exploration and production sector in the United States found rig activity was on the decline.

Shale-rich states like North Dakota are behind the drive in output from the Lower 48. State data, however, show rig activity on the decline. The state's Department of Mineral Resources said there were 166 active rigs as of Wednesday, a 14 percent decline from September.

Data show production from the United States holding steady, however. For the week ending Dec. 26, EIA found Alaskan oil production was down about 6,000 barrels per day, while output from the Lower 48 was steady at 8.6 million bpd.