"Yes, I have made my mistakes and I fully accept responsibility and culpability for those mistakes," McGreevey told about 400 union officials and workers. "I believe in a merciful God."
McGreevey, 47, announced Aug. 12 that he is gay and would resign from office Nov. 15 because he had had an extramarital affair with a man.
During Friday's speech, McGreevey, a Democrat, never mentioned his pending resignation or the scandal. He reminded the audience of his accomplishments, citing state job growth and a booming economy.
At times the event seemed like a campaign rally. McGreevey received standing ovations, and audience members chanted, "four more years."
The appearance, marking McGreevey's resumption of an active public schedule after three weeks of closed-door meetings, came on the day by which the Democrat would have to resign to allow a special November election to replace him. He ignored questions shouted by reporters about the transition of state government and the looming deadline.
McGreevey has said he intends to leave office Nov. 15 and has rejected Republicans' demands that he quit sooner so the special election could be held. A spokesman said Friday the governor had no plans to resign in time for the deadline.
A federal judge has set a Sept. 8 hearing for a lawsuit that seeks a special election regardless of the earlier deadline.
If McGreevey remains in office through Nov. 15, the rest of his term would be served by Senate President Richard Codey. The next regular gubernatorial election is November 2005.