Brogan offered no timeline on when a policy may be considered.
"This is too important to rush," he said.
The proposal was put forth by a task force of board members, university presidents, students, faculty and law enforcement, but the driving force for making the change came from the system's lawyers, who feared that current bans could not survive constitutional challenges. Current practice is to allow each school to dictate whether firearms or weapons would be allowed on its campus.
Several faculty union leaders spoke against the tabled proposal, and called for campuses to be gun-free zones.
"The best policy . . . is to prohibit weapons on all areas of campus unless carried by police, security officers, or other security personnel," said Steve Hicks, a professor at Lock Haven University and president of the Association of Pennsylvania State College and University Faculties.
Justin Amman, student government association president at East Stroudsburg University, urged the board to seek more student input and raised questions about the ability to enforce a policy allowing guns in open areas.
If he were allowed to walk on campus sidewalks with a gun strapped to his hip, he said, "who will stop me at the door to the student union building?"
Also, will metal detectors be needed, he asked.
The 14 state universities also include Bloomsburg, California, Cheyney, Clarion, Edinboro, Indiana, Kutztown, Mansfield, Millersville, Shippensburg, Slippery Rock and West Chester.
Seven of the universities - California, Edinboro, Kutztown, Lock Haven, Millersville, Shippensburg and Slippery Rock - have individually adopted policies that closely mirror the proposal for open-carry in some areas.
Their policies, the first of which was adopted in April 2012, followed recommendations from lawyers for the state system, who said a blanket prohibition was legally unenforceable.
State Supreme Court cases in recent years have struck down blanket bans, though allowing regulation in sensitive places. Brogan noted a Florida appeals court ruling last month that knocked down a gun ban at the University of North Florida.
Kutztown last spring began to allow firearms in open areas of its 289-acre campus in Berks County. The university still restricts weapons in buildings and athletic facilities "or while attending a sporting, entertainment, or educational event on university property or sponsored by the university."
Such narrowly tailored policies have withstood constitutional challenge.
And in 2011, the Virginia Supreme Court ruled that George Mason University's ban on guns in buildings and at events did not violate the Second Amendment. George Mason also is a public university.
Under the Pennsylvania system's proposal, deadly weapons, including firearms, would continue to be banned inside all campus buildings, including dorms, student unions and cafeterias.
They also would be banned from sporting and entertainment events, commencement ceremonies, and other indoor and outdoor areas where large numbers gather, as well as outdoor class meetings, field trips and camps. Deadly weapons include knives with blades longer than three inches, swords, clubs, bows and arrows, explosives and ammunition.