Asked 25 days on the picket line, Washington Hospital Center's striking registered nurses said yesterday they are ready to give up an issue that last week led to their 2-to-1 rejection of management contract offer - their demand for a union shop.

Dottie Hararas, president of the District of Columbia Nurses' Association unit at the Hospital Center, said yesterday that the nurses are prepared to accept an "agency shop" arrangement that would provide for voluntary membership in the union and the compulsory payment of reduced union dues by those who choose not to join the union.

The proposal the nurses intend to present when negotiations resume at 9 a.m. today also provides that the agency shop provision will be put into effect only if more than 50 percent of the 425 nonsupervisory registered nurses at the hospital vote to accept it.

The strike, which enters its 26th day today, has been waged by about 60 percent of the center's staff nurses. The nurses union contends that about 80 percent of the nurses have remained off the job: however, 247 or 58 percent of the nurses, voted June 14 to reject the center's contract proposal.

The Hospital Center has said all along that between 58 and 64 percent of the nurses were not reporting to work, and the center's figure matches the number attending the contract ratification meeting.

The executive committee of the Hospital Center's board of directors is expected to meet at 8 a.m. today, presumably to consider the union's offer, which was unofficially conveyed to committee members yesterday in Mailgrams.

The board voted earlier in the strike to back the management of the Hospital Center fully in its positions at the negotiatings table, including its refusal to compromise on the union shop issue.

The union's agency shop offer represents the nurses fourth compromise on the issue. The union originally demanded a full union shop. Then it offered to allow present employes who did not want to join the union the option of doing so. Then it offered a secret ballot on that question.

Commenting yesterday on the course of the strike Hararas said "We have struggled with apathy," which she said has been typical of nurses. "That is why, no matter what we go into the hospital with,, we are victorious because nurses are no longer apathetic.

"People are saying, 'oh, nurses exist . . . They're not just things in white saving lives. They actually exist," said Hararas.

Yesterday District Mayor Walter E. Washington, who is a candidate for reelection this fall, sent telegrams to the union an the Hospital Center offering to serve as a mediator in the dispute, which is already being mediated byy the Federal Mediation and Conciliation Service.

The nurses "welcome [the mayor's] generous offer" and Hospital Center officials said they "have received the telegram and will be discussing and considering it."