Police on Sunday found a noose tied around the neck of the statue, along with an old Georgia flag with a Confederate battle emblem in its design, which has since been updated to exclude the emblem.
When Meredith tried to enter Ole Miss in fall 1962, Mississippi's governor tried to stop him. That led to violence on the Oxford campus.
U.S. Attorney General Robert Kennedy sent 500 U.S. marshals to take control and days later, Meredith was allowed in the school. Though he faced harassment, he graduated with a degree in political science.
The FBI said Friday it planned to expand the vandalism investigation for potential violations of federal law.
"It is embarrassing that these men had previously identified with our fraternity," said Brian C. Warren Jr., CEO of Sigma Phi Epsilon. "SigEp as a national fraternity has championed racial equality and issues on diversity since 1959 when it became the first national fraternity to invite members of all races, creeds and religions to join its membership."
Warren said the fraternity will conduct a review to ensure that members' values align with those espoused by the organization. "We won't allow the actions of a few men to undermine the more than five decades of leadership this fraternity has demonstrated in the fight for racial equality and diversity on our college campuses," he said.
The university tried Friday to question three white students in connection with the vandalism but their attorneys would not allow that to happen without arrest warrants. The three have not been identified.
University spokesman Danny Blanton said Friday the school's findings have been turned over to the district attorney's office. Blanton said the university will also proceed with internal disciplinary action through a judicial panel that consists of both faculty and students.
The university is satisfied that the three students under investigation are responsible for the statue's desecration, Blanton said.
The Ole Miss Alumni Association is offering at $25,000 reward for information leading to an arrest. University Police Department Chief Calvin Sellers said the reward offer gave police some good leads in the case.
Blanton said it's not yet clear who might share in the reward.
District Attorney Ben Creekmore did not immediately respond to a message left Friday by The Associated Press. However, he told WMC-TV in Memphis that criminal charges would be difficult.
Creekmore said investigators and prosecutors have looked into several misdemeanors, but he said criminal charges were unlikely by his office because the statue was not physically damaged, and the suspects did not appear to be trespassing.
He said federal investigators could opt to bring charges if they saw fit. Creekmore said if new information comes to light, his office could revisit the issue.
Blanton said it's up to state and federal authorities to press criminal charges, but "obviously, since we've seen who is responsible, we want to take swift and decisive action.
"What we want to do is to show this type action can't take place on this campus. We want to demonstrate that we will not tolerate this type behavior," he said.
Ole Miss will move forward "as soon as possible" with discipline through the university's student judicial process. That panel, which consists of both faculty and students, could choose sanctions including dismissal and barring the three from campus, Blanton said.
The fact that the students won't talk to administrators is disappointing, he added.
"We certainly wish they would be forthright and discuss this matter so that we can get to the bottom of it. We want to hear their side. We want to know not just what happened, but why they did it. We want to open a dialogue," he said.
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