Obenshain, a state senator, said he called Democratic nominee Mark Herring, also a state senator, to congratulate him as the end neared for a recount, six weeks after Democrats won the races for governor and lieutenant governor, Politico reported.
"The recount is almost over, and in this contest for attorney general ... it's become apparent that our campaign is going to come up a few votes short," he said.
Early recount results showed Herrington expanding the 165-vote lead he held after the initial vote count, the report said. Herring's campaign said the lead had grown to more than 800 votes by Wednesday.
Democrat Terry McAuliffe defeated outgoing Attorney General Ken Cuccinelli in November to succeed Gov. Bob McDonnell and Ralph Northam, the Democratic nominee, was elected lieutenant governor in November.
Herring's victory gives Democrats all five of Virginia's statewide offices, and deprives Republicans of an office Cuccinelli and McDonnell both held before advancing to become their party's nominee for governor, Politico noted.
However, the victory has the potential to turn control of the state Senate over to Republicans. A special election will be held to choose a successor to Herring in the body, which currently has 20 Republicans and 20 Democrats.