The justices, without comment, on Monday turned away arguments that the law wrongly denies most mature girls under 18 the right to an abortion without parental involvement.
A spokeswoman for Virginina Gov. Jim Gilmore said he was pleased with the court's action.
The action isn't a decision. It doesn't preclude the possibility the court may review the Virginia law, or one similar to it, at some future date.
The 1997 state law requires that unmarried girls under 18 and not living on their own tell one of their parents at least 24 hours before having an abortion.
The law waives that requirement if the girl's doctor has reason to believe she has been victimized by abuse or neglect. And it allows a girl to bypass parental notification by proving to a judge she is mature enough to handle the abortion decision by herself.