Roderick M. Hills, chairman of the Securities and Exchange Commission, has asked President Carter to name his replacement "at an early date."

A Californian Republican, Hills told Carter in a letter that he would "like the new leadership of the commission to be in place by the first of April."

In a letter, dated Feb. 23, and released yesterday, Hills said he is setting the deadline "primarily for the benefit of the commission and in some part for my personal convenience."

Hills' term runs through June 30, but he said he is anxious to return to private law practice. There have been reports that Hills plans to set up law practice here with his wife, Carla, who was Secretary of Housing and Urban Development in the Ford administration.

Hills had submitted his resignation to President Ford, but was asked by the new administration to stay on until a replacement was named. In addition to the chairmanship, there also is a commissioner slot vacant on the 5-member commission.

The Carter administration is considering about a half-dozen names for the vacancies. Reported to be high on the list are Peter Solomon, a managing partner of Lehman Bros., the investment banking firm, and Harold Williams, dean of the business school at the University of California at Los Angeles.

The North American Securities Administrators, an organization of securities regulators from 50 states, Canada and Mexico, have endorsed one of their own for SEC chairman.

William Barnes, who leads the California Securities Commission, was recommended to President Carter in a letter from Hugh Mekins, the Michigan commissioner who is chairman of NASA.

Mekins, in a telephone interview, said it was the first time that the NASA had endorsed anyone for the commission.