Wyatt B. Durrette Jr., a Fairfax County Republican who narrowly lost a bid for Virginia attorney general last month, yesterday removed himself from the contest for the U.S. Senate, saying the strain of another statewide race on his family and finances would be "almost impossible."

With Durrette out of the running, the GOP appears headed for the nomination next June of Rep. Paul S. Trible (R-Va.) to succeed retiring Sen. Harry R. Byrd Jr., an independent who has held the seat since 1965.

Trible, a 34-year-old congressman from Newport News, has spent more than a year courting support for a Senate campaign. Byrd's retirement decision dramatically altered his chances and some Republican leaders this month began seeking an alternative candidate. Their first choice was Gov. John N. Dalton, who consistently has rejected their appeals. Both Durrette and Rep. Stanford Parris (R-Va.) also were approached and this week both bowed out of the race.

Durrette, a 43-year-old lawyer, yesterday praised Trible as "an energetic and constructive candidate and an excellent congressman," stopping short of an outright endorsement. Durrette discounted any dissatisfaction with Trible among party officials: "I think Paul has the potential to put together the broad coalition of support needed to win state-wide," he said.

Former Culpeper delegate D. French Slaughter, a Democrat who first became an independent and then a Republican, said yesterday he still is considering a run for the Senate. Others in the GOP, however, yesterday said that the party's nomination all but belongs to Trible.

Virginia Democrats, meanwhile, have begun a search of their own for what a party leader called a "fresh face" to present as their candidate next November. "The feeling is that we need to present voters with a fresh person, someone who can put together the kind of support we saw last November for (Gov.-elect) Chuck Robb," said William Thomas, a former state Democratic chairman and a member of Robb's inner circle.

"There is a natural tendency in these things to look at people who've held elected office," said Thomas, an Alexandria lawyer. "This time, there's a feeling that we should look beyond that."

So far, the names most often mentioned are former state attorney general Andrew P. Miller of Alexandria, state Senate Majority Leader Hunter B. Andrews of Hampton and state party chairman Owen Pickett of Virginia Beach.

Some Democrats argue that a Trible candidacy might point to the need for a more experienced opponent with a record in state office: "Someone who is a known commodity would have a significant advantage," Arlington Democrat John Milliken said.

Democrats yesterday said they felt no need to rush toward a decision on their nominee since the selection of delegates to the Democratic nominating convention doesn't start until spring. "We don't need to respond with speed," Thomas said.

For their part, the Republicans yesterday appeared to be moving quickly to unite their forces. Trible yesterday welcomed Durrette's decision, praising him as "a bright star in Virginia politics," and noting that "it is important that our party be united at the earliest possible time to move forward to victory."

Durrette yesterday said his decision was "primarily personal." The turning point, he said, came when his 7-year-old son last week expressed a hope that his father would be able to come to his soccer games this spring.

But Durrette, still considered the GOP's most likely 1985 gubernatorial candidate, also indicated a reluctance to divide the party at its Richmond convention next June: "Assuming a candidate has developed a broad base of support, avoidance of an inter-party struggle is desirable," he said. "So far, it seems Trible has support from many different sectors (of the party.)"