Norfolk's three white state senators, in a reapportionment showdown tinged with racial overtones, today narrowly lost an effort to keep their citywide election district -- a move opponents charged would illegally dilute the political power of blacks.

After twice insisting that Norfolk be broken into two single-member districts and defeating the Norfolk senators by one-vote margins, the Senate climaxed a day of parliamentary maneuvering by approving, 29 to 10, a plan reapportioning the seats of its 40 members.

The proposal now goes to the House of Delegates, where it is expected to receive automatic approval from lawmakers who have been more concerned by their inability to agree on a plan to realign the House's 100 election districts.

Once it reapportions its two houses, the General Assembly will attempt to finish carving new districts for Virginia's 10 U.S. representatives by week's end, becoming the first state in the nation to reshape its election districts on the basis of the 1980 Census.

The Norfolk senators, all of them Democrats considered liberals by Virginia standards, conceded today that their city must lose one of its senators to neighboring Virginia Beach. But they argued that their constituents favored allowing both remaining Norfolk seats to be elected on a citywide basis.

The Senator's Democratic leaders -- many of them close personal friends of the Norfolk Three -- said the atlarge district would prevent blacks, who make up 35 percent of the city's 263,000 population, from electing a black senator and thereby open the entire Senate plan to almost certain rejection by the Justice Department. Under the Voting Rights Act of 1965, the department must approve any changes in Virginia's election districts.

"It is with regret that we have to get into the issue of race," said Hunter B. Andrews, the acerbic Senate majority leader who orchestrated today's narrow victory. "None of us wants to but it is here . . . [and] you can bet your last Confederate nickel that the Justice Department is going to say 'Why did you change [to an at-large district]. . . . What was the racial motivation for doing it?'

"I don't agree with the Voting Rights Act," Andrews added, "but it is the law of the land and we must uphold the law of the land."

Norfolk Sen. Peter K. Babalas said later he believed he had had the votes to beat Andrews last week and had agreed to put off the floor fight until today in hopes of reaching a compromise. But Babalas said Andrews and othe members of the leadership had used the time to win over some of the dissidents by revising their new districts to make them more favorable.

"I gave [Andrews] the opportunity of passing out his candy and it caught a lot of people with a sweet tooth," Babalas said.

Andrews also suggested today that if the Justice Department rejected the Senate's reapportionment, he and the committee he chairs would start redrawing lines all over the state to punish dissenters. "Once the can of worms explodes," he warned, "many can be touched."

Despite the Norfolk defeat, the plan may face a court challenge from civil rights groups because it divides the city along a north-south line that Richmond Sen. L. Douglas Wilder, the Senate's sole black member, contended would cut Norfolk's predominantly black neighborhoods in half.

Other blacks, including Norfolk Del. William Robinson Jr., said even the North-South division was preferable to an at-large district. "It's the lesser of two evils," he said.

Ten years ago the Senate carved Norfolk into three single-member districts only to have the plan overturned by the Supreme Court because of discrepancies in counting Navy personnel, who make up about 10 percent of the city's population. The Census Bureau revamped its methods over the last decade and Senate leadership argued there was no longer any rationale for leaving Norfolk with an at-large district while the rest of the state was divided into single-member districts.

Conspicuous by his absence today was Lt. Gov. Charles S. Robb, the Senate's presiding officer and the Democratic Party's certain gubernatorial nominee, who could have broken the tie votes. Robb's office said he was in Northern Virginia for an annual physical examination but some senator suggested he ducked the session to avoid having to vote on politically delicate reapportionment issues.

Separately, members of the House Privileges and Elections Committee today approved a reapportionment plan that preserves most incumbents' districts and grants two new seats to Fairfax County. The proposal, dubbed the "bunny rabbit plan" because one of its districts resembles a rabbit, deviates by as much as 28 percent from the ideal district's population as set by census figures -- a variance that is wider than any plan approved by the Supreme Court.

Several civic and public interest groups have threatened lawsuits if the General Assembly adopts a plan with such a wide deviation.

House leaders hope to bring the new plan, which passed the committee 15 to 5, to a floor vote Wednesday. An earlier effort, which had satisfied almost all incumbents but had inadvertently created one delegate seat too many, was killed today by a unanimous committee vote.