The league released a statement after the meeting Sunday at Georgetown University. The meeting had been scheduled before Syracuse and Pittsburgh announced last month they will leave the conference to join the Atlantic Coast Conference.
The original purpose of the meeting was to discuss the conference's upcoming television rights negotiations, but the defections forced expansion onto the agenda.
"The presidents voted unanimously to authorize the commissioner to aggressively pursue discussions with a select number of institutions that have indicated a strong interest in joining the Big East Conference," Marinatto said in a statement.
Navy, an independent, and Air Force, of the Mountain West Conference, are among the Big East's top targets for expansion. There has been speculation that Temple also could be invited back to the league.
Temple was booted from the Big East after the 2004 season and has found success in the Mid-American Conference in recent years.
The Big East also still has to guard against losing more of its current members.
Marinatto said in the statement that the league's presidents discussed making leaving the conference tougher, without mentioning specifics such as raising exit fees.
"The presidents are also actively considering changes to the conference's governing bylaws to further solidify the membership of the conference," Marinatto said.
TCU is scheduled to leave the MWC and join the Big East for the 2012-13 school year, and has not publicly wavered from that commitment. But the Horned Frogs have been discussed as a possible target for Big 12 officials as they attempt to figure out how to reconstitute the league after Texas A&M's departure to the Southeastern Conference.
The Big 12 also might consider reaching east and adding some combination of Louisville, West Virginia and Cincinnati.
Connecticut's governor confirmed that UConn is interested in joining Pitt and Syracuse in the ACC if it expands further.