Edward M. Kennedy rhetorically indicted President Carter today, implying in a campaign speech that weak leadership in the White House is the reason Congress has not approved legislation designed to stop a nationwide increase in violent crime.

The Massachusetts senator, taking his race for the White House to the Deep South, said that instead of active presidential involvement on behalf of anticrime legislation, "there has not been one statement" on the subject from President Carter. Kennedy spoke to a group of Young Democrats in Charleston.

In essence, he invoked the crime problem as a specific case to prove the general theme of his campaign: what he calls Carter's abdication of presidential leadership.

Kennedy's campaign today went from the Country Music Hall of Fame in cold, rainy Nashville to a pink concrete auditorium on the Atlantic in sunny Miami Beach and then to Charleston.

Kennedy said the rate of violent crime was up 13 percent in the first half of this year. He cited several bills that he suggested might offset the increase. Justice Department officials have worked with Congress on the bills, he said, but "during the past three years there has not been one . . . public declaration" from the president.

All the legislation the senator cited is in the bailiwick of the Judiciary Committee, which Kennedy chairs.

The White House responded quickly.

"I'm accustomed to seeing the president blamed for anything that happens in the world," said press secretary Jody Powell. "But for Sen. Kennedy, who has been a member of the Judiciary Committee for almost two decades and is now its chairman, to blame the president for his inability to get his legislation through his own committee is a step beyond anything I've seen or heard lately."

Powell charged that one measure cited by Kennedy -- a reform of the Law Enforcement Assistance Administration -- has passed both houses of Congress and is in conference committee. In other cases, he said, the failure has not been in the White House but in Congress, including Kennedy's committee.