In a challenge to President Carter, Sen. Edward M. Kennedy (D-Mass.) tonight renewed his call for a moratorium on new nuclear power plant construction and called on Carter to make his own position clear.

Kennedy issued the challenge at a local Democratic fund-raising dinner, his first speech since a presidential commission earlier this week issued its report on the March 28 accident at the Three Mile Island plant in Pennsylvania. The Kennedy Commission report called for safety improvements at the nation's nuclear plants and abolition of the five-member Nuclear Regulatory Commission in favor of a new agency with a single administrator.

". . . I call on the president to make his position clear," Kennedy said. "This nation needs a moratorium on nuclear power plant construction. Until fundamental safety changes are made, no new construction permits . . . should be issued anywhere in the United States."

Kennedy's statement emphasized his longstanding differences with Carter on nuclear power plant construction. Carter, who has spoken out in support of nuclear power in the past, has not taken a position on a construction moratorium, saying he wanted to study the Kennedy panel's recommendations. The commission did not recommend any delay or halt to nuclear construction while its safety recommendations are being considered or implemented.

Kennedy who earlier this week formed a 1980 presidential campaign committee, called for a moratorium on new nuclear power plant construction immediately after the Three Mile Island accident.

A spokesman for Kennedy said later that the senator does not favor halting construction of about 90 plants now being built, providing appropriate safety standards are followed.

Kennedy's decision to speak out against nuclear power in a key coal state carried a number of political overtones, and the senator made no secret of them.

"Thirty years ago, to our regret, we followed the nuclear genie away from the coal fields of West Virginia," he said "Over the past three decades, if we had spent as much on research and development for coal as we spent for our nuclear power, we would now be well on our way to independence from Arab oil."

Kennedy's remarks were made at a Jefferson-Jackson Day dinner attended by all the big-name Democrats of this state, including Gov. John D. (Jay) Rockefeller IV, Senate Majority Leader Robert C. Byrd and Sen. Jennings Randolph.

At a reception before the dinner, Kennedy wasted no time in seeking to link his political aspirations with the successful 1960 effort of his brother, John, in the West Virginia Primary.

"Every Kennedy feels at home in West Virginia," he told his audience. ". . . this is where it really started, back in 1960."

And turning to Rockefeller, Kennedy added: "The one thing I've always resented is someone running for public office on the basis of a famous family name."