Virginia Sen. Harry F. Byrd Jr., the Senate's only independent, said last night he will stick to his plans to retire in January, shunning pleas from conservative supporters to enter what many predicted would be a difficult three-way race.

His announcement came nine days after an influential bipartisan group stunned Virginia political circles with a "draft Byrd" drive that, by yesterday, had collected approximately 23,000 signatures around the state.

In a three-page statement, Byrd, 67, thanked supporters for their efforts, calling the petition drive "unprecedented in Virginia political history." But, he said, the wishes of his wife and "the lateness of the hour" convinced him to adhere to his original decision.

This farewell statement by the veteran senator and heir to the state's most powerful political name--issued 24 hours before the filing deadline for Senate candidates--immediately buoyed the chances of Republican Paul S. Trible, a 35-year-old congressman from Newport News who Saturday won the GOP nomination for the seat.

It troubled some Democrats who had calculated that their nominee, Lt. Gov. Richard J. Davis, would have a better chance in a three-way race. The prevailing political theory had Trible and Byrd dividing the conservative vote, giving Davis a definite advantage.

Yesterday, Byrd said he had let supporters go ahead with the petition drive out of concern over the worsening state of the national economy and the failure to bring government spending under control. "Last November, I thought considerable progress was being made in this direction, but unfortunately that is not the case," said Byrd, who succeeded his father in the Senate in 1965.

Byrd gave few reasons for rejecting the draft initiated by his old friends and supporters, former governor Mills Godwin, a Republican, and former congressman Watkins Abbitt and former state delegate W. Roy Smith of Petersburg, both Democrats. In announcing the petition drive on May 28, Smith said there was "a better than 50-50" chance Byrd would run, odds that Abbitt said had improved to 75 percent last week.

But since the May 28 announcement, the Byrd loyalists have been dismayed by the statewide reaction. In particular, they were caught off guard by editorials in nearly every major statewide newspaper--including the staunchly conservative Richmond Times-Dispatch and News Leader--urging the senator to stay out of the race. An editorial in Saturday's Norfolk Virginian-Pilot, another newspaper that has endorsed Byrd in the past, also asked him to stay out, strongly criticizing him as a senator who has been "mostly absent from the great debates of the past two decades. . . . In the Senate, he is not a leader; he has few strategies and few ideas."

"I know they were dumbstruck by those editorials," said one Republican with close ties to the Byrd camp. "They never expected them."

Many state politicians also believe that Byrd was influenced by developments at Virginia's two political conventions last weekend. Republicans, meeting in Richmond, stood solidly behind Trible as former Byrd ally Sen. Herbert Bateman of Newport News made known the party's displeasure with a Byrd candidacy.

The Democrats' nomination of Davis, a proven statewide vote-getter, may have also figured into Byrd's calculations. More than anything else, political observers said that Byrd and his allies feared defeat in November, a prospect that would have tarnished the senator's unbroken record of electoral victories and spoiled the ending of this chapter in the Byrd dynasty.

Meeting with reporters outside his Washington office after 7 p.m. yesterday, Byrd never strayed from the themes of his prepared statement.

"Gosh, it was really heartwarming," said the diminutive white-haired senator, speaking of the signers of the petitions in almost paternalistic tones, "It also made me feel real humble . . . when the top leaders of the state show such an interest as many of them did."

Byrd's chief backers yesterday put out a statement saying they respected Byrd's decision not to stand for reelection.

Some Democrats traced the conservatives' sudden eagerness to draft Byrd for a fourth term to their dissatisfaction with Trible. Several conservatives admitted openly that Trible's youth and ambition reminded them uncomfortably of J. Marshall Coleman, last year's defeated Republican nominee for governor.

But yesterday some of the key members of the "draft Byrd" drive said they would now go back to supporting Trible. "I shall now revert to being a supporter of Paul Trible's," said former Martinsville mayor Francis T. West, "I think this crystallizes support for Trible."

Upon hearing the news, Trible "was elated--that's an understatement," said a campaign spokesman. In an official statement, Trible, who has been careful to avoid any criticism of Byrd, applauded the senator's decision "not to bow to public demand.

"Rather than succumb to these pressures, split the conservative vote and possibly elect a liberal Democrat in November, the senator placed principle above everything else . . . A two-man Senate race will increase the chances that the Senate will remain in responsible hands," said Trible.

A spokesman for Davis said the Democrat had no reaction "either way," but predicted that Byrd's exit will give Davis a chance to zero in on "Trible's support for Reaganomics as the chief issue in the fall campaign."

The news lifted a pall that had hung over last weekend's GOP convention, threatening to divide the party between old-line Byrd conservatives and loyal party regulars. "Good, good," said Del. Vincent F. Callahan Jr. of Fairfax who was chairman of that convention. "I would say that makes Trible the odds-on favorite to win the election. You've got a clear choice between a liberal and a conservative, and the conservative will win."

Byrd, who had kept even close advisers guessing until yesterday, said he made up his mind "technically, actually, firmly," only a few hours before his announcement. His wife, Gretchen, was, he said, "tremendously happy" about his decision.

J. Smith Ferebee, another Byrd supporter who has been spearheading the petition drive, said he talked to Byrd Sunday night by telephone and that the senator was having a difficult time making up his mind.

"It's a tough one," Ferebee said. "Sen. Byrd is the greatest statesmen that Virginia has had in my lifetime. But he's not going to do anything that he thinks is detrimental to the state. If he runs and wins, he's going to cause some bruised feelings."