The major stumbling block to settlement of New York's 80-day newspaper strike was removed yesterday when the publishers and pressmen's union agreed to let a third party resolve the issue of pressroom staffing.

There was no assurance about when the presses would roll again at The New York Times and Daily News. But mediator Theodore H. Kheel said a settlement was possible "within 48 hours," meaning a resumption of publication early next week. Others said it may take longer.

Meanwhile, Rupert Murdoch, who resumed publishing his afternoon New York Post three weeks ago, alleged that the Times, News and newspaper unions were conspiring to block publication of his planned morning tabloid. As a result, he said, the morning paper may never come out.

The first real breakthrough in the 11-week strike came shortly before 4 a.m. yesterday when Kheel announced that both sides had agreed to submit the pressroom manning issue to a "fact-finder" whose decisions would be binding.

Kheel said the fact-finder will use pressroom staffing levels at the Newark Star-Ledger as a basis for determining requirements at The Times, under a formula that would later be extended to te News and Post. The Post resumed publication under a "me-too" agreement that will incorporate manning agreements made by the other papers.

Until yesterday both sides refused to budge on the manning issue. The publishers contended they needed drastic reductions to compete with more flexibly staffed competitors like the Star-Ledger. The union charged that half of its 1,500 jobs in New York would be jeopardized by the publishers' proposals.

Sources soid yesterday that William Kennedy, president of the pressmen's union, agreed to the binding fact-finding approach after other newspaper craft unions, which have been honoring the pressmen's strike, indicated they might bolt and return to work.

Kennedy told reporters after the 17-hour bargaining session that produced the agreement that it was "an accommodation that had to be made." Asked if he was happy with the plan, he said, "I'm not happy with a strike that's 11 weeks old."

Still to be negotiated were procedures for the fact-finding and a number of contract issues, including whether an earlier agreement on job guarantees for current employes extends to workers at the News' financially troubled color rotogravure plant in Queens. Kheel said yesterday there has been a tentative agreement on the job security issue.

Before the papers can resume publishing, there must also be a contract settlement with several other unions, but sources close to talks said these agreements can be reached with relative ease once the pressmen sign a contract.

The "fact-finding to a conclusion" process is similar to arbitration in that it results in a decision binding on all parties. It is also similar to a procedure used recently to avoid a nationwide strike by postal workers.

Murdoch's conspiracy plaint came three days after the scheduled morning debut of his dime newspaper, the Daily Sun. Publication was thwarted by Murdoch's inability to get contracts with the city's various newspaper unions.

In an announcement published in the Post, Murdoch said: "There appears to be a conspiracy among the drivers union, some members of the Allied Printing Trades Council, the Daily News and the New York Times to prevent the energence of the Daily Sun by Saddling it with oppressive costs . . ."

Douglas LaChance, president of the drivers union, denied the conspiracy charge, as did a spokesman for the News. Said LaChance: "My reaction is to laugh. All we did was to attempt to negotiate a competitive contract. Maybe he thought I'd give him better deal."

Murdoch said publication of the Daily Sun - which was intended to compete with the 20-cent Daily News for the city's tabloid market - was delayed "perhaps permanently."