More than 600,000 liquid propane gas water heaters are being recalled to repair thermostats that have been linked to a series of explosions that have killed five people and seriously injured 16 across the nation, the federal government said yesterday.

The U. S. Consumer Product Safety Commission also announced that the thermostat manufacturer, the White-Rodgers division of Emerson Electric Co. of St. Louis, had agreed to pay a$420,000 settlement for allegedly failing to report the explosions promptly. That is the largest civil penalty in the agency's seven-year history.

A company representative said that Emerson decided to pay the settlement in order to speed the recall program. He said the explosions were reported in January 1980, and that the thermostat problem resulted from abuse by the persons using the thermostat, rather than from a design flaw.

The water heaters being recalled were sold between 1961 and 1980 primarily to homeowners in rural areas where natural gas connections were unavailable. They were sold under a variety of trade names by Sears, Roebuck and Co., A. O. Smith Corp. and other manufacturers and retailers. A Sears representative said yesterday that the company stopped selling the water heaters in February 1980.

Two major Washington-area liquid propane suppliers estimated yesterday that 13,000 of their customers in Northern Virginia and suburban Maryland rely on liquid propane gas water heaters. However, they said they didn't know how many have heaters with the White-Rodgers thermostat.

The commission said that if the pilot gas control knob of the thermostat was damaged, the safety valve could become stuck in the "open" position, allowing the liquid propane gas to escape. Since liquid propane is heavier than air, it can accumulate near the floor rather than escape through pipe vents, the commission said. That could result in an explosion from a variety of ignition sources, including an electric spark, officials said.

Consumers who think their water heater contains one of the recalled thermostats can telephone the toll-free hot-line 800-325-9589 at White-Rodgers for information.

White-rodgers thermostats made since 1976 are "substantially more resistant to damage" and less likely to produce an explosion than the earlier thermostats, the commission said. However, they also are being replaced under the recall program to avoid any risk, the commission said.

The post-1976 thermostats were installed in liquid propane gas water heaters made by A. O. Smith, Rheem Manufacturing Co., W. L. Jackson Manufacturing and State Industries. They were sold by Sears, Montgomery Ward Co. and a variety of plumbing supply outlets.

John Bell, director of media relations for the commission, said the deaths and injuries occured over the last 12 years. But he would not say where they occurred. He said commission attorneys advised against disclosure of that information.

The recall of the propane gas water heaters is expected to cost the three companies signing the agreement as much as $9 million over the next year, Bell said. The three companies are Sears, A. O. Smith and Emerson.

A total of 56 different brand names of water heaters made by the various companies are being recalled. The average retail cost of the water heater was about $200.

White-Rodgers, the thermostat manufacturer, agreed to mail safety alert notices to the estimated 15 million U. S. households now using liquid propane gas. The notices will describe the thermostat which is eligible for replacement.