Democratic Party officials opened three days of meetings here yesterday with a procedural dispute about who will be allowed to vote for new party chairman.

The fight, centering on the status of the 25 at-large members of the Democratic National Committee, was seen as a test of strength in the contest for the chairmanship and is expected to come to a showdown when the full committee meets today.

Election of a chairman is the main item on the agenda this week in the party's first meeting since President Reagan swept 49 states in defeating Walter F. Mondale last November.

Other issues scheduled for debate include an effort to reduce the power of the DNC's special-interest caucuses and composition of a new party Fairness Commission, which is to review rules for nominating a presidential candidate in 1988.

Election of a new chairman is scheduled Friday. Paul G. Kirk Jr., party treasurer and a former aide to Sen. Edward M. Kennedy (D-Mass.), is considered the front-runner, and the fight over the status of at-large members is seen as an effort by his opponents to block his election.

Kirk's opponents said he is close to having a majority on the 378-member committee, and they have seized on the at-large members in hopes of thwarting him. Party sources said that he enjoys support of about 20 of the 25 at-large members and that, if they are not allowed to vote, he might be denied the chairmanship.

His opponents are Nancy Pelosi, former California Democratic chairman; Terry Sanford, former North Carolina governor, and Robert J. Keefe, a veteran Washington political operative.

Kirk's forces won two victories yesterday in the procedural fight. They blocked a rules committee move to deny at-large members the right to vote this week. Then, on a tie vote, the executive committee failed to approve a recommendation to the full committee calling for election of new at-large members at today's meeting.

After the vote, Kirk described his opponents' effort as "normal, last-minute mischief" and predicted that he will win a first-ballot victory.

The rules committee considered two resolutions affecting various party caucuses.

The first, which would have ended their official recognition, failed to receive a seconding vote. "We have become caucus junkies," said DNC member Richard Koster, who sponsored the resolution. "We can't get enough. Cold turkey is the remedy."

A weaker resolution approved for consideration by the full DNC would end the practice of giving each caucus a seat on DNC standing committees.

The Coalition for a Democratic Majority charged yesterday that the caucuses "are destructive of the party" because the public sees them as a "fragmented, balkanized group of special interests rather than the population as a whole."

Neil G. Cashion Jr. of North Carolina, speaking for the Young Democrats, said, "The caucus system has turned a lot of young people away from" the party.

On the Fairness Commission, created after complaints by Jesse L. Jackson and Sen. Gary Hart (D-Colo.) that 1984 nominating rules were unfair, the rules committee approved a resolution offered by Democratic state chairmen calling for 40 of 50 members to be chosen by regional caucuses.

A resolution urging no reduction in the number of convention slots reserved for unpledged, elected officials also won approval.

A resolution from Jackson supporters, calling for "grass-roots" activists to be given 25 seats, died in the rules committee.