Former North Carolina governor Terry Sanford yesterday announced his candidacy for national chairman of the Democratic Party and said the party should change the way it nominates presidential candidates.

Sanford's candidacy is expected to turn the contest for chairman into a three-way race. The other leading contenders are Paul G. Kirk Jr., party treasurer and former aide to Sen. Edward M. Kennedy (D-Mass.), and Nancy Pelosi, former California Democratic Party chairman.

California fund-raiser Duane B. Garrett, one of six previously announced candidates, said yesterday that he is dropping out and will campaign "full time" for Sanford.

Sanford, 67, stepping down as president of Duke University, formally announced his candidacy at a meeting of the North Carolina Democratic Party executive committee in Raleigh. He has strong support from southern party chairmen and former North Carolina governor James B. Hunt Jr. Arizona Gov. Bruce Babbitt yesterday became the first non-southern governor to endorse Sanford.

Earlier, Sanford sought to become the consensus choice of a group of elected officials, led by Babbitt and Virginia Gov. Charles S. Robb, who were seeking to rally the party behind a candidate. After that effort failed, southern chairmen prevailed on Sanford to get into the contest on his own.

The 378-member Democratic National Committee will meet in Washington on Feb. 1 to pick a successor to Charles T. Manatt, whose term is expiring.

"I feel the presidential nomination process needs to be changed," Sanford said in a telephone interview yesterday. He said he hopes to devise a system that would make delegates to the 1988 Democratic National Convention "more representative of voting Democrats" nationally and make the nominating process "deliberative."

He criticized the current "wild and woolly" nominating system for placing undue emphasis on early events, such as the Iowa caucuses and the New Hampshire primary. "Before people can be looked at, they're gone," he said. "We need to develop a process that keeps the candidates in for a considerably longer time."

Sanford said he wants to examine ways "to take the emphasis off the primaries," although he said he would "not do away with primaries."

Saying he is disturbed by the "drift" within his party, Sanford said he would try, as chairman, to develop new and stronger leaders and a "sounder library of ideas and possibilities" for the party.

Sanford dismissed criticism that he is too old for the job. "I'm running full steam at Duke now," he said. "I have as much intensity and drive as ever."

Sanford served as governor of North Carolina from 1961 to 1965 and has been president of Duke since 1969. He ran unsuccessfully for president in 1972 and 1976.

Until Sanford's entry, Kirk was seen as the front-runner in the race. He has the support of eight Democratic governors, including outgoing Utah Gov. Scott M. Matheson, Arkansas Gov. Bill Clinton, Michigan Gov. James Blanchard and his home-state governor, Michael M. Dukakis of Massachusetts.

Pelosi, claiming 125 votes, has the support of New York Gov. Mario M. Cuomo, Maryland Gov. Harry R. Hughes, Los Angeles Mayor Tom Bradley and Manatt.

Garrett, whose fund-raising skills earned him the title of national co-chairman of Walter F. Mondale's presidential campaign, said he quit the race for the party chairmanship because "I basically was dead in the water."

He said he has no agreement with Sanford about becoming the party's finance chairman if Sanford wins. "There's no deal; there's no commitment," said a source familiar with the discussions the two have had over the past month.