DURHAM, N.H. — An anonymous donor has agreed to pay up to $20,000 to cover expenses the town incurs as a result of a visit by President Obama, said Jay Gooze, the chairman of the Town Counci, said Sunday.

The town asked that local expenses for Monday’s Obama campaign stop be covered by the president’s reelection campaign. Durham officials had said that the visit is expected to cost the town an extra $20,000 to $30,000 in overtime.

Obama is scheduled to speak Monday at Durham’s Oyster River High School.

The Obama campaign had responded to the request by saying that all decisions on security expenses ‘‘are exclusively within the control of the appropriate government officials’’ and that if there are further questions about allocation of the expenses they should be directed to the Secret Service.

On Sunday, Gooze said the town’s request was not motivated by partisan politics and most Durham voters are registered Democrats.