Cuccinelli's stance on the proposal reverses that of his predecessor, who is now a Virginia Supreme Court Justice, The Washington Post reported Wednesday.
Only married couples and single men and women, regardless of sexual orientation, can currently adopt in Virginia. The proposed changes would require private and faith-based groups to allow gay parents to foster or adopt children.
In a memo, Cuccinelli's office said the proposal "does not comport with applicable state law and public policy."
"Therefore the State Board [of Social Services] lacks the authority to adopt this proposed language," wrote Allen Wilson, senior assistant attorney general.
The change in regulations was proposed by former Democratic Gov. Tim Kaine in November 2009, less than two months before he left office to take the chairmanship of the Democratic National Committee.
Cuccinelli, a Republican, angered gay-rights activists last year when he urged the state's public colleges and universities to rescind policies banning discrimination on the basis of sexual orientation.