It was an interesting -- and contrasting -- political weekend: The largely conservative Republicans were exploring ways to draw more blacks into their party and the Democrats were pursuing a sensitive reassessment of the influence of blacks in their party.

The Democrats met here to discuss party rules for next year's elections, but their overriding concern was the exodus of whites from the party in recent elections. Republicans, meeting in Staunton, gingerly were exploring modest overtures to blacks in hopes of cracking their traditional alliance with Democrats.

State GOP Chairman Donald Huffman said he is considering a move to establish an official but nonvoting seat for blacks on the party's ruling State Central Committee. Other seats may go to Hispanics and Asian Americans.

"I don't want to get off into a quota system . . . . This idea does carry with it that threat," Huffman said.

The party also approved $4,000 to send state GOP officials to training seminars on how to attract more minority participation.

Wyatt B. Durrette, a Richmond lawyer and former Fairfax County legislator who is considered the front-runner for his party's gubernatorial nomination, said he intends to seek more than token black support.

In October, Durrette stayed for the full state NAACP convention in Roanoke and held about 2 1/2 hours of private meetings with black leaders.

"There's a far higher degree of agreement on important issues . . . than either Republicans or blacks realize," Durrette said during the weekend. "We thought they weren't listening so we didn't talk. They thought we weren't talking so they didn't listen."

And GOP officials pointed out that the party's share of black votes, while still relatively small, rose sharply in last month's elections.

President Reagan's share of the black vote rose from 3.4 percent in 1980 to 8.2 percent this year while Republican Sen. John W. Warner got 21.2 percent of black votes, triple his 7.1 percent share in 1978, according to Larry Sabato, a University of Virginia professor and elections analyst.

That was the best showing since 1977, when Republican J. Marshall Coleman won as state attorney general with 32.7 percent of black votes in a race against a conservative Democrat who had supported "massive resistance" to school desegregation, according to Sabato.

The renewed interest by the largely conservative Republicans, who insist that black voters are not monolithically liberal, also comes at a time when party leaders still say racial prejudice is likely to keep blacks from winning statewide office in Virginia.

"Relatively speaking, I personally believe . . . in the state of Virginia . . . they may well have a problem," said Huffman.

Huffman was responding to questions from reporters about the campaign of Democratic state Sen. L. Douglas Wilder of Richmond, who is black and the only announced candidate for his party's nomination for lieutenant governor. At the same time, a half-dozen white Republicans and one little-known black businessman are angling for their party's nomination for the second spot.

Huffman, who praised Wilder as a "confident, articulate individual," suggested that his party's candidates will attack Wilder as "a liberal." He said he doubted that "liberal" would become a code word for any veiled racist appeal. "I don't think you have to use code words at all," Huffman said, noting that the news media would make it clear to all voters that Wilder is black.

Huffman said he believed the Democrats "are in a real box" over Wilder's candidacy. Huffman said many white Democrats are concerned that a black cannot win statewide but fearful that any attempt to deny Wilder's nomination would be seen as antiblack and create risk of a boycott by black voters, who usually make up about a third of the Democratic vote.

Wilder and other black legislators were angry at reports that a group of white legislators, including state party Chairman Alan A. Diamonstein of Newport News, met privately to discuss the statewide elections and the impact of Wilder's candidacy. Diamonstein, a party moderate, said the absence of blacks at the meeting was an oversight.

The white legislators are said to be concerned that they may lose seats in the 100-member House, now controlled 65 to 34 by Democrats with one independent, as well as about the races for governor and attorney general.

Several have endorsed a call by Senate Majority Leader Hunter B. Andrews for Gov. Charles S. Robb to become more publicly involved in the party's nominating process.

Robb, a moderate who cannot by law succeed himself, has urged the national Democratic Party to move toward moderation but publicly has largely stayed out of a similar battle in his state. Robb has scheduled a news conference for Tuesday at which, his aides said, he will respond to questions about his role in the party.