Peace Corps Director Carolyn R. Payton resigned under protest yesterday.

In a letter of resignation presented to President Carter early last evening, Payton said:

"I deeply regret that I am required to offer you my resignation as Peace Corps director, effective immediately.

"During my 13 months in office, I have attempted to direct the Peace Corps so that it would fulfill its mandate . . . I have not succeeded in part because of conditions which had arisen before you and I took office, and in part because there have been deep differences between the Action administrator and the Peace Corps over the interpretation of this mandate.

"Unfortunately, these differences could not be reconciled; and I could not continue as director."

Action Director Sam Brown, who has jurisdiction over the Peace Corps, VISTA (Volunteers in Service to America) and other volunteer service programs, had earlier this week requested Payton's resignation because of "policy differences," according to Peace Corps and other administration sources.

Payton, through a spokeswoman, strongly implied Thursday that she would not step down unless told to do so by the president.

Yesterday, according to a White House spokesman, Payton met with Robert J. Lipshutz, counsel to the president, "to discuss policy differences which seemed to be unreconcilable with Sam Brown.

"Lipshutz said he also discussed with her the president's feelings that her resignation was best for all concerned," said the spokesman, associate press secretary Marc T. Henderson.

In a statement on Payton's resignation, Carter said: "I have come to the conclusion that there are unresolvable policy differences between the director of ACTION and the director of one of its major agencies, the Peace Corps.

"In order to carry out the important programs of ACTION and to resolve this serious impasse, I am today accepting the resignation of Dr. Payton as director of the Peace Corps."

The president said his acceptance of the resignation "does not in any way reflect on the competence, integrity or sincerity of Dr. Payton."

"I wish to express my appreciation to her for the good service which she has rendered," Carter said.

Brown issued a statement saying he appreciated "the contributions Dr. Payton has made to the Peace Corps." He added, "I continue to believe that the Peace Corps is the best opportunity we have for assuring that American assistance reaches the people with the greatest need around the world."

Payton's action yesterday ended several days of rumors and leaks that she was planning to and had, in fact, resigned under pressure. It also ended months of bitter wrangling with Brown that, according to several sources, reached a climax early this month at a meeting of Peace Corps North, Near East, Asia and Pacific countries directors in Morocco.

The sources said Payton and Brown got into a dispute over the Peace Corps fiscal 1979 budget. Payton allegedly felt that $95 million, up from $85 million for fiscal 1978, was insufficient to carry out present operations and introduce new ones.

"The Morocco conference was the final kind of rising to the surface of the problems between Carolyn and Sam," one source said. Other differences between the two involved administration of the Peace Corps, the sources said.

Despite numerous attempts, neither Payton nor Brown could be reached for direct comment.

In her letter of resignation, Payton said: "The issue between the director of ACTION and me is an issue of substance about the Peace Corps, and not one of my sex, color, or age."

Payton, 53, was the first woman director and the first black director of the Peace Corps. She joined the agency in 1954, and later was its director of operations in the eastern Caribean. She left in 1970 to become director of the Howard University counseling service, and was nominated by Carter last year corps director.