The decision came a day after university officials announced they would move the statue of Confederate President Davis from the center of its campus in Austin, but allow the statues of other Confederate figures, including one of Robert E. Lee, to remain.
The Davis statue is scheduled to be installed at the University of Texas Briscoe Center for American History, where officials have said that it will become part of an educational exhibit.
A site for the Wilson statue, which will be relocated to maintain symmetry on the campus' Main Mall, has not been determined.
On Saturday, a spokesman for the Sons of Confederate Veterans said the decision to remove the statues within 72 hours had not given the group proper time to investigate the university's legal authority to do so.
"These statues have stood in place for 82 years, and we are a little concerned about the speed that the university has decided to relocate them," spokesman Marshall Davis told the Los Angeles Times. "The Briscoe Center won't be ready to receive the statue for 18 months, so what's the hurry?"
According to court filings, the group also said that the university decided to relocate the statues without approval from the Texas Legislature, State Preservation Board or the Texas Historical Commission.
But university spokesman Gary Susswein said the move to relocate the Davis statue was the right course forward and consistent with the law.
"We are confident we will move ahead with these plans," Susswein said in a statement Friday. Under state law, he said, universities have the authority to relocate statues on their campuses.
The university has agreed to wait to move the statues until a hearing is held next week.
The debate over Confederate symbols has raged since the massacre of nine parishioners at a historical black church in Charleston, S.C., in June. Confederate symbols appeared in photos of Dylann Roof, who is charged in the killings, later prompted the removal of the Confederate flag at the South Carolina Statehouse.
On Friday, Louisiana Gov. Bobby Jindal announced he would investigate his authority to block the removal of four Confederate monuments in New Orleans.