Federal authorities have reinstated a finding that Virginia Tech violated a law requiring colleges to issue timely warnings of threats to students and staff when the university responded to the 2007 massacre on the Blacksburg campus.

But Education Secretary Arne Duncan, in a decision issued last week, ordered a smaller fine than the $55,000 initially levied against Virginia Tech. The final amount has not been determined but will exceed $27,500.

Whether the university violated the campus safety law in its response to the gunman who killed 32 people and then himself on the morning of April 16, 2007, has been a question for more than two years. Virginia Tech, which disputes the finding of fault, says it is strongly considering an appeal to federal court.

The case has been under scrutiny as universities across the country have beefed up emergency-response systems. At Virginia Tech, those systems kicked into gear Dec. 8, minutes after an assailant fatally shot a police officer. There were e-mails, text alerts, robo-calls and sirens. A blunt advisory told the campus community: “Stay inside. Secure doors.”

That rapid lockdown was a sharp contrast to the response in 2007.

At issue in the federal probe was a mass e-mail the university sent at 9:26 a.m. that day, about two hours after police found two students fatally shot in a dormitory but a few minutes before the rest of the victims were gunned down in another building.

In the initial alert, the university said that a “shooting incident occurred at West Ambler Johnston” dorm; that police were “on the scene and . . . investigating”; and that the community was “urged to be cautious and asked to contact Virginia Tech Police” with information about the case or anything that seemed suspicious.

Seung Hui Cho, a mentally ill student from Fairfax County, started firing at students and instructors in Norris Hall soon afterward. An official timeline prepared for Virginia officials found that this second phase of Cho’s attack began about 9:40 a.m.

Critics say that an earlier and more detailed warning about the first two shootings, which occurred about 7:15 a.m., coupled with a campuswide lockdown would have saved many lives. University officials reject the second-guessing and insist that their actions were consistent with the best information available at the time from police.

The federal investigation centered on the timeliness and content of the initial alert and whether Virginia Tech followed its own safety policies.

In May 2010, the Education Department issued a preliminary finding of fault that was later confirmed. In March 2011, the department set a fine of $55,000, the maximum possible for two violations of the law.

But an administrative judge at the department overturned the fine a year later, finding that the 9:26 a.m. alert complied with the law, known as the Clery Act.

“This was not an unreasonable amount of time in which to issue a warning,” Judge Ernest C. Canellos wrote in March. “If the later shootings at Norris Hall had not occurred, it is doubtful that the timing of the e-mail would have been perceived as too late.”

Duncan disagreed.

In a 12-page decision dated Aug. 30, Duncan wrote that during the two-hour interval, the university “had not located the suspect, had not found the weapon and was confronted with the distinct possibility that the gunman was armed and still at large. Faced with this possibility, the [university] should have resolved any doubts it had regarding the timing of the warning by issuing the warning before 9:26 a.m.”

Duncan reinstated a $27,500 fine related to that finding and wrote that the department should issue a lesser fine for issues related to what he termed “inconsistent policies.”

But his might not be the final word.

Virginia Tech spokesman Larry Hincker said of Duncan’s decision: “Once again, the higher-education community has been put on notice that timeliness is situational and will be determined by department officials after the fact. The federal government has never defined a timely warning and continues to hold universities accountable even when a university’s actions are well within the department’s own guidelines.”

Hincker said in a statement that university President Charles W. Steger plans to confer with state Attorney General Ken Cuccinelli II about an appeal to federal court, which the spokesman termed “a strong possibility.”

The VTV Family Outreach Foundation, which represents many families of victims and survivors of the massacre, praised Duncan’s decision but said it is time to move on.

“Everybody needs to get beyond this,” said Joe Samaha of Centreville, president of the foundation. His daughter Reema was an 18-year-old freshman when Cho shot and killed her. “At some point, these appeals need to stop and people need to be allowed to heal. That’s the bigger story in my mind — for Virginia Tech just to be able to move forward and actually be able to work together to make sure this type of tragedy doesn’t happen again.”