The Interior Department this week awarded more than $2 billion in oil drilling leases off the Alaskan coast although the Federal Trade Commission still was reviewing possible antitrust problems with many of the leases.

Sources said the FTC -- which by law must be consulted on whether federal leasing programs constrain competition -- was concerned that any leases awarded to British Petroleum, Standard Oil (Ohio), Atlantic Richfield Co., Shell Oil Co. and Exxon Corp.--the dominant companies in the crude oil market on the West Coast -- would lessen competition.

Those companies, or joint ventures in which they participated, won about 80 percent of the 121 leases awarded by the Interior Department this week in the oil-rich waters known as the Diapir Field.

Justice Department officials said Assistant Attorney General William F. Baxter, head of the antitrust division, gave the Interior Department verbal clearance to award the leases on the grounds that they would not "create or maintain a situation inconsistent with the antitrust laws."

They also said that the Justice Department met its legal obligation to "consult" with the FTC, although the commissioners had signed off on only a small portion of the leases awarded this week.

The commission gave clearance last week to about 25 leases for which companies other than the five dominant firms placed the high bids, officials said. However, the FTC still is reviewing the possible impact on the crude oil market of awarding leases to those five companies, and the commission was unaware that Baxter had given the Interior Department the go-ahead until the day after the leases were awarded.

Baxter gave permission to award the leases -- worth $2 billion for the federal treasury -- within two weeks after the bids were received on Oct. 13. Federal law, however, allows the Justice Department and the FTC 30 days to review the bids, and some commission officials questioned why Baxter acted so quickly, without giving the FTC more time to comment.

Baxter could not be reached for comment.

Thomas J. Campbell, director of the FTC's bureau of competition, said yesterday that the FTC will continue to investigate. If it finds antitrust problems with the leases, it could seek a court order to block them, he said.

In 1980, the FTC raised antitrust objections to another sale of drilling rights off the Alaskan coast. "An undue increase in the reserve holdings by dominant firms in the market may further enhance the power of these firms and thereby lessen competition in the region," it said.

Those leases were awarded despite FTC objections, however. "Nobody need heed our advice," Campbell said.

Sources said the FTC is examining whether awarding the leases to the five largest crude oil producers in the region will decrease overall competition. The commission wants to insure that no company or group of companies could monopolize the crude oil market, although that threat is lessened by the present glut.

Another concern is whether the companies have used their dominance of the market in the past to hold back supplies, to favor certain refiners and retailers and to control where the oil is sold, the sources said.

As of 1980, BP and its affiliate, Sohio, owned 49.2 percent of the Trans Alaskan Pipeline, the only source of transportation from Alaska's North Slope. Arco owned 21 percent, and Exxon 20 percent, the FTC said.

Interior Secretary James G. Watt hailed the sale as a sign of the success of his offshore oil development program.

Critics, however, pointed out that only a small portion of the tracts -- those believed most lucrative by the industry -- accounted for most of the $2 billion bid by competitors.