Arizona Gov. Bruce Babbitt (D), seeking to play a larger role in reshaping the Democratic Party, announced yesterday in Phoenix that he will not seek reelection as governor or run for the Senate in 1986.

Babbitt's decision not to run for the seat of retiring Sen. Barry Goldwater (R) was a blow to Democratic hopes of recapturing the Senate next year and makes Rep. John S. McCain III (R), a two-term House member and former prisoner of war in Vietnam, the favorite to succeed Goldwater.

Babbitt, who has been talking with friends about a possible 1988 presidential race, said that he was "eager to be a part of the debate over the future of the party" and preferred to stay in Arizona rather than uprooting his family to move to Washington.

"I'm just not temperamentally ready, for family and personal reasons, to pull up my roots and start all over again in Washington," Babbitt said. "It's just not in me."

Since President Reagan's landslide victory in November, Babbitt has actively involved himself in national Democratic Party activities. He was one of several governors who unsuccessfully sought to draft a "consensus" candidate for Democratic National Committee chairman, and he has spoken out on the need for the party to get away from its "cathedral of orthodoxy" on policy.

He was one of the principal organizers of the Democratic Leadership Council, a group of mostly southern and western elected officials that was founded last month to stimulate policy debate. That group has been seen as a challenge to the power of DNC Chairman Paul G. Kirk Jr., who plans to establish his own policy council.

Babbitt, acknowledging that McCain would have been a "formidable" Senate opponent, said that he decided not to seek a third term as governor because he preferred "to keep moving."

"I now see that it is very possible for a western governor to have a major voice in the national party without living in Washington," he said. "I wasn't certain of that a year ago."

Babbitt said he had no "present intentions" about a 1988 presidential candidacy. He said that he plans to establish a Washington-based foundation later this year for research, policy, direct mail and political advocacy.

Sen. George J. Mitchell (D-Maine), chairman of the Democratic Senatorial Campaign Committee, said he was "not surprised" by Babbitt's decision and expressed optimism that the Democrats could capture Goldwater's seat.