Minnesota Democrats, emotionally wrought over the death of Sen. Paul D. Wellstone (D-Minn.), yesterday began the search for a new candidate to run in his place in an election that could determine whether Democrats or Republicans control the Senate in January.

Former vice president Walter F. Mondale, who represented Minnesota in the Senate when the Democratic Farmer Labor Party dominated Minnesota politics, quickly emerged as the leading choice of many Democrats to replace Wellstone on the November ballot.

Asked whether he was interested in seeking the Senate seat, Mondale, who will turn 75 in January, said, "I just want to spend today mourning," but he did nothing to dampen speculation that he might accept, if offered, the opportunity to run in Wellstone's place.

Mondale, who served as Jimmy Carter's vice president and was the Democratic presidential nominee in 1984, was encouraged by many Minnesota Democrats yesterday to consider running to give the party a chance to maintain its slender hold on power in the Senate. National labor leaders and other Democratic senators also were pushing to have him named as the replacement, with one Democrat saying that AFL-CIO President John Sweeney believed that "the notion of Mondale carrying on the fight was a good idea."

Wellstone's death marks the second time in a month that a competitive Senate race has been thrown into turmoil. Last month, New Jersey Sen. Robert G. Torricelli (D) suddenly dropped out of his reelection campaign after polls showed him a likely loser because of ethics problems. He was replaced by former senator Frank R. Lautenberg, 78, now favored in the race.

Democrats hold a one-seat margin in the Senate and Wellstone was one of three incumbent Democrats, all from the Midwest, in competitive races. But of the three, the liberal Wellstone was considered in the best shape in his race against former St. Paul mayor Norm Coleman.

The other midwestern Democrats in close races are Sen. Tim Johnson of South Dakota and Sen. Jean Carnahan of Missouri. Carnahan was appointed to the Senate two years ago after her husband, then-Gov. Mel Carnahan, died in a plane crash a few weeks before the election but remained on the ballot and won the election over Republican John D. Ashcroft.

Republicans also have three seats in jeopardy, two held by incumbents -- Sen. Wayne Allard of Colorado and Sen. Tim Hutchinson of Arkansas -- and an open seat in New Hampshire.

Strategists and spokesmen for both parties refused to speculate publicly about how Wellstone's death might affect the Minnesota race and thus overall control of the Senate, although there was some agreement among independent analysts that Democrats might benefit from a sympathy vote of the type that occurred two years ago in Missouri.

"Whoever becomes the Democratic nominee becomes instantly competitive and the dynamics are unpredictable," said Steven Schier, a professor at Carleton College in Minnesota.

Under state law, Democrats have until next Thursday to name a replacement for Wellstone. Minnesota law then allows for the printing of a supplemental ballot that would list Coleman and a new Democratic candidate for Senate. That ballot would be given to all voters on Election Day along with the ballot for all other races.

Mike Earlandson, the chairman of the Democratic Farmer Labor Party, said he has received conflicting legal opinions of what would happen if the party fails to name a new candidate. But he said, "It is my intention to call a meeting of the executive committee before Thursday to consider our situation. Senator Wellstone would want us to do everything in our power to see that a Democrat wins the election and is in his seat when the Senate convenes in January."

Many Minnesotans already have voted by absentee ballot and there was confusion about how those ballots will be handled. One interpretation was that any absentee ballots marked for Wellstone will not be counted, but those for Coleman will be counted, which in a close election would put Democrats at a disadvantage. Democratic strategists said, however, that anyone who voted absentee for Wellstone will have the right to vote in person on Election Day and expressed the hope that most of Wellstone's most loyal supporters would do so.

Wellstone's death also has potential implications for the pending lame-duck session of Congress. Gov. Jesse Ventura (I) has the authority to fill the vacancy created by Wellstone's death. Ventura appeared briefly before the cameras and declined to say what he might do, or when, offering only that he would not appoint himself to the vacancy. Ventura earlier announced that he would not seek reelection to a second term.

One option open to him is to leave the seat vacant until the election and then immediately appoint the winner to fill the vacancy during the lame-duck session. That would give Republicans immediate control of the Senate until January, even if the outcome of the battle for the Senate were to keep the body in Democratic hands.

The focus on Mondale underscored two realities about the Minnesota Democratic Party. One was the consensus among Democrats that, if possible, they need to find a candidate of significant stature to replace Wellstone on the ballot. Mondale, who served as ambassador to Japan during the Clinton administration, fills that requirement.

The other reality is that Minnesota Democrats have been in decline for more than a decade. Their candidate for governor four years ago, Hubert H. "Skip" Humphrey III, the son of former vice president Hubert H. Humphrey, won just 28 percent of the statewide vote. Although Mark Dayton defeated an incumbent two years ago to capture the state's other Senate seat, the party has few strong or recognizable candidates who could step in under these extraordinary circumstances.

Nonetheless, several other names were the topic of speculation yesterday. Among them were Alan Page, the former Minnesota Vikings star defensive tackle who is now a member of the Minnesota Supreme Court. Page, however, would have to resign from the court to run for the Senate. Two years ago, when he was approached to run for the Senate, Page declined.

Despite his loss two years ago, Humphrey was considered another possibility, having a well-known name in Minnesota politics and statewide experience as former state attorney general. Mondale's son Ted is another potential candidate, as are Mike Ceresi, who lost the Democratic Senate primary to Dayton two years ago, and Ann Wynia, who lost a race for the Senate in 1994.

But none of them have the stature of the former vice president, whose politics are probably closer to Wellstone's than virtually any other possible Democratic candidate. Whether Mondale is willing to give up a comfortable life in Minnesota, where he continues to practice law and enjoy his family, is uncertain. But some Democrats speculated that Mondale's political competitiveness and strong party loyalty could tempt him to trade that life for a return to a Senate in Democratic hands.

Democrats were counting on Wellstone's grass-roots appeal and organization to help him prevail in a tight election. Whether that same passion will exist in behalf of another candidate, even one with the standing of Mondale, was unanswerable yesterday.

Balz reported from Washington, Broder from St. Paul. Staff writer Jim VandeHei also contributed to this report.

Former vice president Walter F. Mondale speaks to Sen. Paul D. Wellstone's supporters at campaign headquarters in St. Paul, Minn., after news of Wellstone's death. Minnesota Republican Senate candidate Norm Coleman, who was challenging Wellstone, talks to reporters.