The oil industry put in bids yesterday totaling $427 million for lucrative tracts off Alaska's southwest coast as the Interior Department proceeded with Secretary James G. Watt's program of offering extensive offshore areas for oil and gas development.

Watt hailed the bidding as a signal of "the strong desire industry has in exploring and developing Alaska's frontier areas . . . . "

He said the $427 million in high bids exceeded by 40 percent the amount predicted by congressional budget analysts. This was the third sale of oil and gas development rights off the Alaska coast under Watt's plan.

Interior officials said the sales have raised $2.8 billion plus royalties.

The plan has come under heavy criticism from Watt's critics, who contend that it calls for putting too much of the nation's energy resources on the market at a time of sagging prices.

But Interior officials have pointed to intense industry interest in the Alaskan sales as reason for proceeding with the plan, which will offer 1 billion acres of offshore waters--virtually the entire American coastline--for leasing in the next five years.

The leases offered yesterday, which will not be issued until they are reviewed by the Justice Department's Antitrust Division, lie in a 2.7-million-acre area known as St. George Basin, where Interior is scheduled to hold two more lease offerings in 1984 and 1986.

State officials had sought a postponement because the basin includes the nation's second largest fishery and is subject to severe weather conditions. The officials dropped their objections in return for commitments to environmental safeguards offered by Interior. But environmentalists remained opposed.