TRENTON, N.J. ? High-level New Jersey Democrats said Sunday that pressure was building among members of Gov. James McGreevey’s own party for him to step down before his announced Nov. 15 resignation date.

A senior administration official and a Democratic consultant, both speaking on condition of anonymity, said several top Democrats were worried an FBI investigation into the governor’s same-sex relationship with a former aide would expose more politically damaging details.

“There’s a deepening concern that it will get uglier and more damaging to the party. It’s pressure for sooner rather than later,” the consultant said.

Since McGreevey admitted having an affair with another man and announced his resignation Thursday, Republicans have called on him to step down immediately to prompt a special election to complete his term, which expires in January 2006.

If McGreevey leaves office Sept. 3 or later, Senate President Richard Codey, a fellow Democrat, would serve the remainder of the governor’s term.

Several Democrats are pressing McGreevey to leave before Nov. 15, but not necessarily before the September deadline, the consultant said.

“There’s a big push on now to get McGreevey out sooner rather than later,” the administration source said.

McGreevey’s lawyer triggered the FBI probe by claiming the aide tried to blackmail the governor, first by demanding $50 million to avoid a sexual-harassment lawsuit, then asking for the governor’s help in developing a private medical college, according to sources close to McGreevey.

The FBI plans to investigate every aspect of McGreevey’s relationship with that aide, a law enforcement source speaking on condition of anonymity told The Associated Press Sunday.

Sources close to McGreevey have identified former aide Golan Cipel, an Israeli national, as the unnamed man with whom the governor acknowledged having an affair.

State Sen. Raymond Lesniak, one of the governor’s closest advisers, said the governor would not leave before his announced date and denounced calls for him to step aside.

In an interview published Sunday by the Israeli daily newspaper Yediot Ahronot, Cipel maintained that he was not gay and said McGreevey repeatedly made unwanted sexual advances.