DETROIT — Prosecutors made a “limited-time offer” Friday to Mayor Kwame Kilpatrick: Resign by Sept. 3 in exchange for the dismissal of one of two assault charges against him. Mr. Kilpatrick rejected the deal, which a mayoral spokesman dismissed as grandstanding.

Attorney General Mike Cox’s office offered the plea deal to the mayor, who also is charged with perjury and other counts in a separate case dealing with his sworn denials of an affair.

“It’s an offer we feel would satisfy the ends of justice,” special prosecutor Doug Baker told reporters outside the courtroom. “And if it can settle the case, then we would be happy with it. If not, then we go to trial.”

Mr. Kilpatrick, Detroit’s mayor since 2002, is accused of shoving a sheriff’s detective into another investigator while they tried to serve a subpoena on a friend of Mr. Kilpatrick’s on July 24. A not-guilty plea was entered at the 38-year-old Democrat’s arraignment Friday.

The assault counts, which came after the perjury indictment, intensified calls for leaders in both parties for the mayor to resign.

Defense attorney James Thomas told reporters the mayor’s legal team rejected the offer, which he called “gratuitous.”

“We’ll consider anything they have to say that’s reasonable,” Mr. Thomas said.

“This so-called offer was made by someone who has no authority to request such a thing and was done purely to score points in front of the cameras,” mayoral spokesman Marcus Reese said in a statement. “We suggest the attorney general resign from running for governor with this weak and frivolous case.”

Mr. Baker made the offer to Mr. Thomas in the courtroom before the arraignment, Mr. Cox’s spokesman Rusty Hills said.

“It’s a limited-time offer, and they’ve got … now until Sept. 3 to say ‘yes’ to the deal,” Mr. Hills said. “We’re the attorney for the people. It’s a good deal for the people. It’s a good deal for the city. We think, ultimately, it’s a good deal for all the parties involved.”

Conviction on the assault charges carries a sentence of up to two years in prison.

Mr. Kilpatrick and his former top aide, Christine Beatty, were charged in March with conspiracy, perjury, obstruction of justice, and misconduct in office, mostly tied to their testimony in a civil trial.

Sexually explicit text messages between the pair, published by the Detroit Free Press in January, contradict their sworn denials of an affair, a key point in the trial last year involving a former deputy police chief.

Mr. Kilpatrick faces prison sentences ranging from up to five to 15 years if convicted of conspiracy, perjury, misconduct, and obstruction of justice charges.

Democratic Gov. Jennifer Granholm has scheduled a hearing for Sept. 3 on the Detroit City Council’s request that Mr. Kilpatrick be removed from office. Final motions before the hearing are due by the close of business on Monday.

Ms. Granholm, who has the power to remove elected officials for misconduct, declined on Friday to discuss anything involving Mr. Kilpatrick.

The next legal question confronting the mayor involves his possible presence at next week’s Democratic National Convention, which could boil down to whether a judge changes Mr. Kilpatrick’s bond in the assault case to allow out-of-state travel.

Wayne County Circuit Court Judge David Groner is expected to hear a bond motion Monday afternoon by Mr. Kilpatrick’s legal team. But the mayor — who also is a convention superdelegate — has not publicly indicated whether he even wants to go to the convention in Denver.

“I’m not sure if he’s made his mind up,” Mr. Reese said Friday.

Brent Colburn, Michigan spokesman for Senator Obama, has said the focus of the convention should be on the presumptive presidential nominee, “not a distraction involving the troubles of one individual.”