The D.C. Democratic State Committee last week urged the City Council to speed up efforts to resolve the District's continuing elections mess, but got a cool response from a key member of the council.

The state committee also formally opposed a proposal to give the D.C. Board of Elections and Ethics more time to clear up its problems by putting off until 1984 school board and Advisory Neighborhood Commission elections now scheduled for later this year.

Several members of the state committee, including national committeewoman Sharon Pratt Dixon, who sponsored the resolution, said the city's hard-won right to elect its own officials should not be sacrificed because of the board's administrative chaos.

Dixon, who supported Patricia Roberts Harris in her unsuccessful campaign for mayor last year, said the council and Mayor Marion Barry should be held responsible for the elections problems.

The council is considering several proposals to reform the city's election system, including proposals for partial re-registration and a broad range of other election changes.

Council member William R. Spaulding (D-Ward 5), longtime chairman of the government operations committee, which has oversight of election issues, largely dismissed the Democrats' critical vote.

"Let them run their business and I'll make sure the city government operates," Spaulding said during D.C. Del. Walter Fauntroy's public birthday party at the Convention Center Friday night.

Some of the Democrats have specifically criticized Spaulding for not moving quickly on Barry's nomination of former council chairman Sterling Tucker to head the elections board and the nomination of Valerie Burden to fill a second vacancy on the three-member panel.

After several weeks of delay and private negotiations with council members, Barry sent the nominations to the council on Feb. 24.

Last week, Spaulding announced he would hold hearings on the nomination March 28 and that his committee would vote on the appointments on April 14.

"That's too much time," said one Democrat who also attended the Fauntroy party, noting that the tardy board appointments are holding up preparations for the next election.

The new board's first order of business will be to hire a permanent executive director to run the demoralized agency.

William Lewis, general counsel to the board, has been serving as acting executive director of the office since last November. He has told friends that he wants to give up the job soon.

Lewis succeeded David A. Splitt, director of the Office of Documents, who had agreed to serve only temporarily in the post during October and November.

Splitt had been filling in for Teddy Filosofos, the Buffalo elections official who was brought in last May to finally clear up the chaotic voter registration rolls and restore order to the office's other operations.

Filosofos abruptly resigned in October, citing political interference and frustrations with the job.

On another subject, the Democrats voted to support an anti-apartheid bill that would prohibit the city from investing pension or other funds in firms that do business in South Africa.

Council member John Ray (D-At Large), who introduced the bill, held two days of hearings on the measure last week.