In a statement Wednesday, Jacobs cited "multiple health problems" as a factor in Levy's resignation, but did not provide further details.
Levy has been under federal investigation for embellishing his Army service in Vietnam.
"The circumstances surrounding his resignation include multiple health problems, but were precipitated by a pending Federal Department of Veterans Affairs investigation," Jacobs said.
Last fall, the Press of Atlantic City reported that the Vietnam veteran's claims that he was a member of the Green Berets were untrue. He apologized, but federal authorities have been looking into whether the 64-year-old Levy made that claim to increase his veteran's benefit payments.
Jacobs said in the statement that the mayor was in discussions with the U.S. Attorney's Office about resolving the investigation in a "fair and expeditious" way. Levy allegedly took in about $25,000 in extra benefits payments as a result of the falsification.
No part of the investigation includes allegations of Levy's abuse of his position as mayor, his lawyer said.
Levy served in the United States Army for 20 years, form 1964-1984 and served two tours of duty in Vietnam, from which he received multiple medals, awards and citations, according to Jacobs.
"The pending investigation has called into question two of those awards, neither of which appear to be supported by an appropriate military order," said Jacobs.
Members of the city council had asked a judge to declare the mayor's office vacant and clear the way for the council president to take over as interim mayor.
Levy — who was missing for almost two weeks — was at home after leaving a Somerset County clinic known for treatment of substance abuse and mental health issues, according his lawyer.
Tuesday's revelation about Levy's whereabouts came after a brief conference with a state judge, who scheduled a Friday hearing to discuss a request by a city councilman to declare that the mayor had abandoned his office.
