If Mayor John DeStefano Jr. has his way, the violence that hit the downtown area earlier this month could spell the end of one of New Haven’s storied institutions: the QPac bus.

At a Tuesday press conference on the city’s recent efforts to contain downtown violence, DeStefano also took on liquored-up students and called for greater cooperation between the city and the universities that bus thousands of young people to downtown night clubs and bars each weekend.

Standing at the intersection of College and Crown streets, the mayor said he questions the value of busing 2,500 undergraduates to the downtown area to party. Universities’ shuttles, though valuable because they reduce drunk driving, have become a license for students to get “fall-down drunk,” he added.

DeStefano said his goal is not necessarily to get rid of the buses, but to work with universities to change undergraduate behavior, adding that he will not have a concrete plan until he speaks with university administrators about discouraging unhealthful drinking habits.

“Frankly, [the universities have] stepped away from any responsibility for policing this behavior,” he said.

Quinnipiac University spokeswoman Lynn Bushnell said in an e-mail that student safety is of “paramount importance” to the university and that it will work with the city on its future efforts to improve security downtown.

“If there are steps we can take to further ensure the safety of our students as they travel in and out of New Haven, we would surely discuss that with the appropriate parties,” she said.

In addition to Quinnipiac, Southern Connecticut State University, among others, buses students to downtown New Haven on weekend nights.

Still, DeStefano said, the biggest problem is not the students, but the clubs they frequent, and he renewed his call for clubs to pay their share of “Operation Nightlife.” The initiative, which the city launched last week in response to a gunfight that erupted Sept. 19 on College Street, cost the city $15,000 in overtime pay this weekend, DeStefano said, equivalent to $800,000 in taxpayer dollars in a year. The clubs should share that burden, he said.

By comparison, DeStefano said, the Crown Street nightclub Static, formerly known as Oracle, paid less than $1,000 in city taxes last year. Static could not be reached for comment Tuesday night.

Club owners have not exactly been cooperative, he said, and have had an “antagonistic” relationship with the city, often denying any responsibility for what happens when patrons leave their establishments.

“This attitude is totally out of whack,” DeStefano said. “The clubs don’t get it.”

Over the weekend, the city fire marshal shut down two bars, Humphrey’s East on Humphrey Street and the Pearl Lounge on East Street for fire code violations as part of Operation Nightlife. In addition, the NHPD stopped 15 people for underage drinking and seized eight fake IDs, New Haven Police Chief Frank Limon said.