The Postal Service and unions representing most of its organized workers bargained past the expiration of their contract at midnight last night in an attempt to reach a new labor agreement and avoid a nationwide strike.

Negotiators continued to bargain on an hour-by-hour basis, and early today the talks were still under way.

The presidents of the American Postal Workers Union and the National Association of Letter Carriers, which represent 500,000 of the Postal Service's organized employes, had threatened earlier to call a nationwide walkout at midnight yesterday if they had no new contract.

That threat was repeated yesterday evening after the unions' governing board rejected a second Postal Service wage offer that postal officials had called "substantially different" from a three-year wage-free proposal presented by government negotiators Friday.

Morris (Moe) Biller, APWU president, and Vincent R. Sombrotto, president of the NALC, jointly dismissed the Postal Service's second offer as a "further insult to our 500,000 members."

Details of the proposed package were not know.

The union leaders said that if the government failed to improve its offer before midnight they would be forced to call a strike -- even though such an action would be illegal. However, at 11:59 last night, federal mediator Nicholas Fidandis said that the "clock has been stopped" on the negotiations, and that the two sides would continue talking.

Sombrotto and Biller frequently had tempered their strike threats with caveats that they were willing to bargain past the deadline if the government made a "serious" proposal.

While most of the attention was centered of the "main table" negotiations going on at the L'Enfant Plaza Hotel, representatives of two smaller postal unions -- the Mail Handlers Division of the Laborers' International Union and the National Rural Letter Carriers Association, which have about 100,000 workers -- were meeting across the street for separate bargaining talks.

Earlier it was reported that talks with these two unions were proceeding smoothly. However, neither had reached an agreement as of midnight.

The two larger unions were seeking a 41.3 percent to nearly 50 percent increase in wages and benefits over the next three years, with the exact figure depending on several variables, including inflation. The current, average annual pay (excluding benefits) for a postal worker is $21,146 annually, according to the Postal Service.

Postal officials rejected the proposal of the larger unions as too costly.

Assistant Postmaster General Walter E. Duka, citing the "obvious sensitivity of this matter," declined last night to discuss details of the new wage and benefits offer. But he said it was "substantially different" from the one offered Friday and "contains new concepts."

The second pay offer was introduced at about 5:05 p.m. yesterday, nearly two hours after Biller and Sombrotto called a news conference to complain that the management team had been absent from the bargaining table for most of the day.

The two union leaders threatened to call a nationwide strike at midnight last night if Postal Service negotiator stayed away from the table.

State and local union officials worried privately last night that the talks might drag on for more than one day beyond the deadline, which they said some of their members would not tolerate.

One APWU official, speaking privately, said rank-and-file members in militant areas such as New York City already were upset because Postmaster General William F. Bolger delayed negotiations seven weeks in legal maneuvering before the National Labor Relations Board.

Bolger asked the board to restructure the bargaining process. It refused.

"Our people thought Bolger was just picking a fight with them. They didn't like it. And they won't like it if they have to give Bolger any more time to do what he could have been doing all along," the APWU official said.

Federal law prohibits strikes by postal employes, who in 1970 and 1978 staged wildcat strikes. The 1970 walkout, involving nearly 200,000 workers at its height, was the largest by federal employees.

Though Bolger and other postal officials continued to express confidence yesterday that they could settle their labor differences without a strike, they also continued to prepare for one.

Duka said the Postal Service's contingency plan included provision for the postmaster general to suspend the private express statutes that give the Post Office a monopoly on the delivery of first-class mail.

Suspension would allow private firms to deliver mail that the government could not handle. But Duka and other officials cautioned that suspension of the statutes would occur on an as-needed basis -- for example, in Washington, New York or other high-volume-mail areas.

The Postal Service also has standby plans to use the military to move the mail, as it did in 1970.

The Post Office handles 360 million pieces of mail daily. Postal officials said customers should continue normal use of the mails.