Members of the second largest postal union rejected the proposed new contract yesterday, ignoring the Carter administration's anti-inflation goals and reviving prospects of a nationwide mail strike.

A walkout could come by next Tuesday, although efforts were underway to avert it.

The contract was rejected by a 78,288-to-58,832 vote of the National Association of Letter Carriers, one of four unions that negotiated the new three-year pact with the U.S. Postal Service late last month.

The agreement provided for a 19.5 percent increase in pay over three years, one of the lowest union wage packages negotiated in recent months and the only major victory thus far in the administration's efforts to slow the pace of wage increases.

The NALC, which represents roughly 180,000 of more than 500,000 unionized postal workers, was the first union to vote and is bound by its constitution to strike if bargaining is not resumed within five days - even though postal strikes are illegal under federal law.

Caught between the conflicting requirements of the law and his union's constitution, NALC President J. Joseph Vacca called on Postmaster General William F. Bolger to reopen contract talks "on or before" next Monday.

At a press conference, Vacca refused repeatedly "on advice of counsel" to say whether the union would strike on Tuesday if Bolger refused to return to the bargaining table by then. Two weeks ago, however, he said he would have no choice but to follow his union's constitution and call a strike.

Bolger, who said two weeks ago he would "absolutely" not resume negotiations, issued a statement that appeared to be deliberately ambiguous on the point."

"The law provides a clearly defined procedure for such situations as this: fact-finding and binding arbitration," said Bolger, "and we intend to comply fully with the law." He made no mention of returning to the bargaining table, and an aide said there were no plans to do so.

At the same time, Wayne L. Horvitz, head of the Federal Mediation and Conciliation Service, set up separate meetings with both sides to "discuss what steps should be taken."

Horvitz did not indicate whether this might lead to a resumption of talks, and thus a strike reprieve, but sources indicated no firm action is likely until votes are counted later this week from the American Postal Workers Union the largest postal union, representing 300,000 workers.

The four unions, also including the relatively small Mailhandlers Division of the Laborers International and Rural Letter Carriers, are not bound to act in unison, according to Vacca. However, a strike by a union as large as the Letter Carriers could cripple service and a picket line could keep other unions away from work.

The last postal strike occurred in 1970, when 200,000 workers walked off their jobs and the mail was handled by federal troops. A similar contingency plan is now under consideration by the Postal Service.

At his press conference, Vacca blamed the rejection vote on "badgering" by the Postal Service, "interference" by White House inflation fighters and AFL-CIO President George Meany's statement earlier this month that the contract didn't contain enough money.

Obviously upset with Meany, Vacca said he would ask the AFL-CIO to beef up the union's meager strike fund, noting tersely, "I think perhaps Mr. Meany might help us after he destroyed it." He called Meany's statement "very detrimental" to the contract.

James La Penta of the Mailhandlers Union, who was secretary to the bargaining committee, said wages were not an issue until Meany and the inflation fighters made it one. The unions' main goal in negotiating the contract had been preservation of a nolayoffs clause and cost-of-living protections, which were achieved.

Both union officials and the Postal Service predicted to the end that the contract would be ratified, despite a prediction by Meany that it would be rejected and recommendations against the pact by national conventions of both the NALC and APWU.