Former Attorney General Andrew P. Miller today joined former Gov. Linwood Holton, former U.S. Navy Secretary John Warner, former national Republican cochairman Richard D. Obenshain and seven other Virginia politicians in a crowded and wide open race for the U.S. Senate seat of retiring Republican Sen. William L. Scott.

Miller, announcing his candidacy for the Democratic nomination in a news conference, declared he is the only one among the seven Democrats in the field who has a chance to defeat a GOP nominee.

Democratic leaders are searching for a nominee to put an end to recent Republican dominance of statewide races. Virginia is the only state that has failed to elect a Democratic governor or senator in the past 10 years.

Both major parties will nominate candidates at state conventions in early June. The Republicans have traditionally nominated candidates in conventions, but the Democrats are abandoning a primary this year in hopes that a convention will pick a winner with less acrimony and cost to party contributors.

Opposing Miller in the state Democratic convention in June are expected to be state Del. Carvington Williams and state Sen. Clive L. DuVal II, both of Fairfax, former Fairfax supervisors Fred Babson and Rufus Phillips; state Sen. Hunter B. Andres of Hampton, and Flora Crater of Falls Church, an independent candidate for lieutenant governor in 1973.

Running in the Republican convention will be Holton, Obenshain, state Sen. Nathan H. Miller and Warner, who is married to actress Elizabeth Taylor.

When Democratic Party policy makers decided last month to hold a convention instead of a primary, some blamed the state's voter registration and primary electian laws, in part, for the Democrats' recent string of losses.

Voters do not register by party in Virginia and Republicans are therefore free to vote in Democratic primaries. Moreover, primary election laws do not provide for runoffs. As a result it was believed that the winner in a race of seven Democrats might get the nomination with as little as 30 percent of what is expected to be a small voter turnout.

Neither party has adopted final rules for delegate selection, but both will choose delegates at city and county mass meetings in the spring.

Miller today opened his campaign as the "most electable Democrat" by saying: "Polls which I have had access to in recent months show that I could defeat any of the Republican contenders in the general election. These same polls show the precise opposite with respect to the other candidates for the Democratic nomination. Thus, if the party wants to select a standard bearer who can win in November, the choice is clear."

It is the second time in two years that Miller has sought his party's nomination for statewide office. In last year's Democratic gubernatorial primary, he also argued that he was the most electable candidate, but primary voters narrowly nominated former Lt. Gov. Henry E. Howell.

Howell was decisively defeated in the general election by Republican Lt. Gov. John N. Dalton.

Miller took note of the decade of Democratic losses in senate and gubernatorial contests and warned that the 1978 Senate race offers the party its last opportunity in the 1970s to break Republican dominance.

He also warned the party's "prospects for success in 1978 are uncertain." He said the Senate candidate would be hurt by a failure to field strong Democratic House candidates in the 10 congressional districts. However, he said, the party "has yet to identify a strong candidate" in half of those districts.

To improve the chances of a Democratic Senate victory. Miller called on the party to do three things between now and the nominating convention in early June: (1) The congressional district party organizations should decline to nominate House candidates unless they are clearly able to make a strong campaign. (2) The state party should raise enough money to make the maximum contribution to the Senate campaign allowed by federal law. (3) The seven Democratic candidates for the Senate nomination should conduct a preconvention campaign that will not divide the party for the general election.

After his primary defeat last year. Miller blamed his loss in part on Howell's charge that he was not competent to be governor and on a suggestion by Howell that Miller had courted support from anti-Semites.

Miller ignored these charges during the campaign, but said after the election that he should have answered them to prevent some voters from gaining the impression they were true.

Miller, 45, appeared for his announcement today accompanied only by his wife, Doris. His news conference had been heralded only by a hand-written note tacked to the door of the Capitol pressroom. He said he had assembled no staff for his nomination campaign and has made no specificcalculation of his fund-raising needs or capabilities.

All of this is in sharp contrast with the extensive and fully staffed campaign that Miller waged in losing to Howell last year. He spent about $1.1 million in that race, a record for a primary in Virginia. In the wake of the defeat, he and his top advisers were criticized for draining party giver and then spending the money ineffectually.

Miller said he does not believe his primary loss to Howell will dull his image with Democratic convention delegates as the candidate most likely to win in November.

Miller repeatedly described himself today as a "responsible progressive who is in the mainstream of the state's Democratic party." He declined several times to say in general terms how his voting record could be expected to campare with that of Virginia's conservative incumbents in the Senate, independent Harry F. Byrd Jr. and Republican Scott.

On specific issues, Miller said he could not vote for ratification of the proposed Panama Canal treaties in their present form. He said he wants assurances of U.S. rights to defend the canal and to put its ships through the waterway ahead of other countries.

He said he still supports ratification of the proposed Equal Rights Amendment to the U.S. Constitution but opposes efforts to extend might give some states the opportunity to rescind past approval.

Miller resigned his attorney general's office to run for governor and since his defeat has been a partner in a large Richmond law firm.