The chairman of the Republican National Committee said yesterday it would be futile for Virginia Republicans to attempt to unseat Virginia Sen. Harry F. Byrd Jr., the Senate's only independent.

The statement by the RNC's Richard Richards came a day after Virginia Democrats scored a stunning sweep of the state's top offices and months of maneuvering by members of the Virginia GOP to force Byrd into their party. Before Tuesday's elections, Virginia Republicans were threatening to oppose Byrd if he decides to seek reelection as an independent.

But Richards' comments, at a breakfast meeting with reporters in Washington, appeared to dampen the plans to challenge Byrd, who has been courted by President Reagan.

"Harry Byrd is comfortable with the philosophy of the Republican Party and is not comfortable with the philosophy of the Democratic Party," said Richards. "But I don't know why Harry Byrd needs to change parties . He's going to win no matter what."

Byrd had no comment on Richards' statement, but a spokesman for his office said the senator will announce his reelection plans next week. The senator, whose father was for years head of the state's Democratic political organization, was appointed to the Senate as a Democrat in 1965. He was reelected in a special election the following year, but in 1970 left the Democratic Party and has won reelection twice as an independent.

Some Virginia Republicans yesterday were still speaking of a Byrd challenge. "Our road back," said state party vice chairman John Alderson, "is to choose a strong and able and attractive candidate for the Senate and put all our energies behind him."