The Interior Department on Tuesday approved Anadarko Petroleum’s plan to drill 3,675 new natural gas wells in Utah’s Uintah basin after a 41 / 2-year approval process that involved Native American tribes, state agencies and environmental groups.

Anadarko said it plans to spend $10 billion drilling the wells over the next decade, doubling its natural gas production in the area to 1 billion cubic feet a day and creating as many as 2,900 jobs, directly and indirectly, during construction.

The approval covered an unusual number of wells and marshaled support from an unusual range of interest groups. In addition, the Obama administration, battered by oil industry criticism of its pace for issuing leases on federal lands, highlighted the approval and the jobs it will create.

The action doesn’t open any new land for production, because the drilling will take place on leases­ already owned by Anadarko. But the step by Interior assuaged some in Utah, where shortly after taking office President Obama had canceled 77 leases issued by President George W. Bush.

Interior Secretary Ken Salazar issued a statement saying the agreement would “uphold America’s conservation values, while bringing growth to Utah’s economy and further reducing our dependence on foreign oil by developing our resources here at home.”

“This is great news for Utah, great news for that region and great news for us as a company,” Anadarko spokesman John Christiansen said. “We have every reason to be excited about it.”

The drilling plan also has the support of the Wilderness Society and the Southern Utah Wilderness Alliance. The new drilling, much of which would be done from existing drilling pads, would disturb the surface of an additional 5 percent of the 163,000-acre parcel of government land, the Interior Department said.

Even though the Uintah basin is not a shale gas region, Anadarko said that it will use hydraulic fracturing to tap natural gas. “Without hydraulic fracturing, the tight sandstones that are about 8,000 feet below the surface will not allow the resource to flow to the wellbore,” Christiansen said.

The additional 500 million cubic feet a day of natural gas that Anadarko would produce amounts to about 0.6 percent of total U.S. natural gas production.

Christiansen said the Interior approval was “relatively unique because of the various interests” involved — covering state, tribal and federal lands. “This is a new model for coming up with a balanced development plan that addresses considerations from a gamut of sides.”

Even the American Petroleum Institute, which has sharply criticized Obama, said the approvals were “very positive news.” But Erik Milito, API’s director of upstream issues, said the industry still wants “more of a streamlined process.” He said that “the administration should not be complaining about the industry ‘sitting’ on leases­ when the government sits on project approvals.”

Interior said the drilling plan includes measures to “safeguard air quality and protect crucial big game winter range, sage-grouse and sage-grouse habitat, sensitive soils, visual effects and recreational use.”

It also said that the development would create an annual average of 1,709 jobs directly and 1,212 indirectly. It would support an average of 875 long-term jobs over the production life of the project.

Although natural gas prices have collapsed to levels not seen in a dozen years, Christiansen said Anadarko will go ahead with development. He said that about a quarter of the production in the area is made up of natural gas liquids — such as butane, propane and ethane — that are more valuable than methane, which is known as dry gas. Though most energy company stocks fell Tuesday, Anadarko’s stock rose 13 cents, or 0.19 percent, to $69.10 a share.