A city spokesman said that it would comply with the judge’s order but added that no specific date had been set for the removal of the tarps. The spokesman, Brian Wheeler, said that police officers were patrolling the monuments on Tuesday evening in case people tried to remove the shrouds on their own.

The judge’s order was a small but significant development in a nearly yearlong legal battle over the future of the two statues, which were erected in separate public parks in the center of Charlottesville in the early 1900s. Months before the white nationalist rally, the City Council voted to remove the Lee statue, as well as to redesign and rename the park with the Jackson monument. That decision led several groups, including the Virginia Division of Sons of Confederate Veterans, to sue the city last March to block those efforts.

And over a weekend last August, hundreds of white nationalists flocked there to protest the removal, waving Confederate flags and chanting Nazi-era slogans as they marched through the University of Virginia campus and converged on Robert E. Lee Park. A day of clashes between the group and counterprotesters grew increasingly violent, resulting in the death of a woman when a man drove a car into a crowd of counterprotesters.

After her death, the City Council voted to cover the two Confederate statues out of respect. Before his ruling, the judge had denied previous attempts to force the city to uncover them, saying that they could remain temporarily. But Judge Moore scolded city leaders on Tuesday for what he called an “after-the-fact attempt” in recent weeks by the city to claim that the plan had always been for the shrouds to stay for one year.