The first round of rhetorical assaults between Virginia's newly nominated U.S. Senate candidates laid the basis this weekend for what is expected to be one of the most vitriolic statewide campaigns in recent years.

As Andrew P. Miller accepted the Democratic nomination, having defeated seven opponents at the party's state convention Saturday night, he called his conservative Republican opponent "an extremist" who 'lives in the 18the century." At another point he said that Republican Richard Obenshain's philosophy "can best be described as consisting of two gears - park and reverse."

Obenshain responded in an interview yesterday by saying, "Andy apparently has schooled himself in the political rhetoric of Henry Howell. I guess he's decided, 'If you can't beat them, join them."

Howell is the former lieutenant governor who defeated Miller in an abrasive Democratic primary for governor last year and then lost to conservative Republican John N. Dalton in November after an equally bitter race.

"We saw last fall what a negative impact on the people of Virginia a mean, biting campaign has," Obenshain said.

The agrressive initial campaigning by Miller contrasts with his style last year, when he ignored Howell suggestions that he was "incompetent" and was courting racist supporters. At the end of that campaign, Miller said that it was a mistake not to respond to Howell because "some voters apparently took his charges at face value."

Miller's public statements of recent days, including his acceptance speech, also make it clear that the defeat six years ago of moderate Democratic senator William B. Spong by conservative Republican William L. Scott is influencing Miller's decision to run a tough campaign against Obenshain.

It is Scott's retirement that is opening up the Senate seat being sought by Miller and Obenshain.

At a time when Obenshain was state GOP chairman, Scott upset Spong by portraying him as a liberal supporter of big federal government and of busing school children to achieve racial balance.

When Obenshain called Miller a "liberal" shortly before his nomination, the Democrat responded by saying, "We're not going to let them get away with that this year. We're ready to play hardball this time."

Obenshain also reacted skeptically yesterday after Miller invited moderate Republican supporters of former governor Linwood Holton and former Navy secretary John W. Warner to vote for him as an alternative to Obenshain, who, Miller said, is outside the GOP mainstream.Obenshain beat Holton, Warner and state Sen. Nathan H. Miller in the Republican race.

"That's a healthy amount of wishful thinking on his part," Obenshain said. "Lin and John and Nathan have all expressed to me personally the strongest interest in campaigning for me this fall. We all saw at our convention what an amazing degree of unity there was when it was over."

Both Obenshain and Miller have tried at the outset of their race to link the other to political figures they believe are unpopular with the state's voters.

Obenshain portrays Miller as a political ally of Howell and President Carter. Miller in his acceptance speech blamed Obenshain for the election of the controversial Scott and said, "We're not going to let him forget it."

Obenshain said yesterday, "I doubt that a retiring senator is going to be much of an issue in this campaign. The real issue is going to be a person continuing in office, Jimmy Carter."

Miller, on his part, dismissed the importance of Howell and Carter as factors in his race.

"I think the primary last spring delineated the differences between me and Mr. Howell" Miller said yesterday in Williamsburg, where he spent most of the day meeting with campaign advisers.

Miller said he had no plans to ask Carter to campaign for him. During the seven years that I was attorney general I stood on my own two feet," he said. "I intend to exercise that independence in the U.S. Senate. Sometimes I agree with Carter and sometimes I disagree. The last thing Virginia needs in Washington is someone with a knee-jerk reaction to vote 'no' on everything Carter proposes."

Miller's first major campaign event is a June 17-27 trip to the Middle East, Greece and Belgium for briefings. The last Democrat who ran for the Senate from Virginia, retired Adm. Elmo R. Zumwalt, former chief of naval operations, also made a trip overseas after getting the nomination for his ultimately unsuccessful race against Sen. Harry F. Byrd Jr. (I-Va.). Zumwalt visited Eastern Europe.

Miller said he intended to continue the type of descriptions of Obenshain that he used in his acceptance speech Saturday night. "Obenshain has built a career on being a political mechanic," he said yesterday. "I, on the other hand, have been a public servant."

Each candidate estimates his campaign will cost at least $1 million.

It appears certain that the Senate campaign will be partly played out in public debates between the two articulate Richmond lawyers. Miller called for debates in his acceptance speech and Obenshain said yesterday, "I'm looking forward to it."