Mayor Vincent Gray adjusts his glasses August 3, 2012. (Daniel C. Britt/The Washington Post)

A mayor’s gift to thousands of District workers — Christmas Eve off with pay, or double pay for those who have to work — has rankled police and firefighters, who are excluded from collecting the bonus.

On Dec. 20, Mayor Vincent C. Gray (D) declared in an e-mail that he would “administratively close” District government on Dec. 24. The e-mail said that the order “does NOT apply to sworn members of MPD” — the Metropolitan Police Department — of which there are about 3,900 officers. A later memo also excluded more than 1,700 firefighters.

And so not all was peace and goodwill on Monday. The head of the firefighter’s union said he plans to file a grievance over the Christmas Eve pay issue; the police union’s chief said Gray’s order proves that the administration has “nothing but disdain” for police and firefighters.

Gray’s chief spokesman, Pedro Ribeiro, said police and other first responders are expected to be on the job nights, weekends and holidays and called it disingenuous for them to demand compensation for doing their jobs.

Ribeiro said Gray “wanted to thank the average District government worker — someone who works in the DMV or someone who works in the Office of Planning — for really stepping up their game this year and improving service.”

He said other workers’ contracts state that they get extra pay when the District is “administratively closed,” and he said police officers typically earn more money and have better benefits than other employees.

“The officers of the MPD do a great job,” Ribeiro said. “We’re happy to sing their praises. But this wasn’t meant for them.”

The dispute played out against a backdrop of long-simmering ill-will between the police union, led by Kristopher Baumann, and the police department, led by Chief Cathy L. Lanier, who is appointed by the mayor.

The two have feuded for years, each accusing the other of trying to undermine their respective camps.

Baumann said the issue has nothing to do with the contract. He said officers last got extra pay for an administrative closure for former president Gerald R. Ford’s funeral in 2007.

Capt. Ed Smith, president of Local 36 of the D.C. Firefighters Association, said he has gotten no answer from the city about why his members are excluded from extra pay. “It’s a morale issue,” he said. “All the other city employees are benefiting from this.”

President Obama also gave federal workers the day off.