Secretary of State Edmund S. Muskie announced yesterday that he has persuaded Warren M. Christopher to remain as his chief deputy until the November presidential elections.

Christopher served as deputy secretary to Cyrus R. Vance. After Vance's resignation last month in protest over the ill-fated Iran rescue mission, there was widespread speculation that Christopher would be named secretary.

When President Carter chose Muskie instead, Christopher said he believed Muskie would be best served by a deputy secretary of his own choosing and indicated that he wanted to leave the department after a transition period.

However, both Carter and Muskie made clear they wanted Christopher to remain, particularly to help maintain contnuity in administration foreign policy. And Muskie released a statement yesterday saying Christopher had agreed to stay "at my request."

The statement added: "As you know, soon after my designation, he made the perceptive and graceful suggestion to me that I freely consider someone of my own choosing to succeed him as deputy secretary. Warren Christopher is that choice. He has agreed to stay with us through the general election in the fall."

Department sources said Muskie plans for Christopher to assume responsibility for much of the day-to-day administration of the State Department. That would free Muskie to concentrate on advising the president on foreign policy and being the administration's principal spokesman in conveying the policies to the public, Congress and foreign governments.

There also is a hope that Christopher's continued presence will help stem a possible exodus of Vance's loyalists from the State Department. And it is hoped he will dampen continuing specualtion about whether control of administration foreign policy has passed to Carter's national security affairs adviser, Zbigniew Brzezinski.

Christopher, a former Los Angeles attorney, became deputy secretary at the outset of the Carter administration. During the presidency of Lyndon B. Johnson, he served as deputy attorney general and Carter considered naming him attorney general after Griffin B. Bell left that office last summer.

Sources said that, in agreeing to stay at State, Christopher did not ask for or receive any promises that he would be given any Cabinet post if Carter wins reelection in November. They said Christopher's intention now is to return to private life and his reason for specifying November as a departure time was to give Muskie the opportunity to choose a new deputy if Carter wins a second term.