The Washington Star employes' unions, complaining that "Time Inc. put a gun to our heads," appealed to The Star's management yesterday to withdraw its threat to shut down the newspaper and permit labor negotiations to continue beyond a Dec. 31 deadline.

Time Inc., the publishing company that took over The Star earlier this year, has warned it will close down the newspaper on New Year's Day unless the unions have accepted stringently modified new five-year contracts before then. Although some Star employes say they regard management's warning as a bluff, most union leaders at the newspaper appear to be taking the threat quite seriously.

George W. Hoyt, The Star's publisher, has been quoted in a union newspaper as saying, "Without new contracts, we're out of business, We'll shut down The Star permanently Jan. 1." A Star spokeswoman confirmed that Hoyt had been quoted accurately.

Union leaders say Hoyt has told them the newspaper's financial losses now amount to $10 million a year -- about as big a deficit as The Star was reportedly running in 1974 when it was taken over by Texas businessman Joe L. Allbritton. Allbritton sold the newspaper to Time Inc. this year for about $28 million.

According to union officials, The Star's management is currently seeking major changes in contracts governing the newspaper's 1,270 unionized employes, including freezes in basic salary schedules for news, advertising and other white-collar employes and severe reductions in its blue-collar work force. Ina statement issued at a news conference yesterday afternoon, the unions denounced these as "union busting" proposals.

Hoyt, a Time Inc. executive who was named Star publisher last June, issued a statement after the union leaders' news conference, saying, "We are actively engaged in collective bargaining with the unions and have no public statement to make at this time."

Colleen Mueller, The Star's promotion and public relations director, said the newspaper would neither confirm nor deny that its current losses amount to $10 million a year. After checking with Hoyt, she said, "It may very well have come up at the Oct. 23 meeting (which union officials had with Hoyt). There were a lot of confidential financial figures that came up at that time."

The Star currently has 14 separate contracts with 11 unions, representing news and commercial employesm printers, pressmen and other workers. All of these contracts are scheduled to remain in effect until late next year, but the newspaper's management is seeking to replace the existing contracts with new agreements that will guarantee five years of labor stability. Time Inc. has said it will invest $60 million in the newspaper during the next five years if acceptable labor contracts are concluded by Dec. 31.

The statement issued by the unions yesterday cited the large number of contracts under negotiation and wide differences between the unions and management over their proposed terms in asking Time Inc. to lift its Dec. 31 deadline. "The logistics alone of settling 14 contracts under the timetable of management's argificial and arbitrary, imposed deadline boggles the mind," the statement said.

Despite the unions' call for removal of the deadline, union leaders expressed pessimism that management would agree. Asked whether she believed the deadline would be lifted, Dorothy A. Struzinsky, the chief negotiator for the Washington-Baltimore Newspaper Guild who acted as a spokeswoman for all 11 unions at yesterday's news conference, replied, "At this time we do not." The news session took place beneath a canopy in front of the main entrance to The Star's Southeast Washington headquarters on a rainy afternoon.