NEW ORLEANS — The city’s director of homeland security on Friday pushed back against his counterpart in Baton Rouge after he said that a drop in emergency grant money should be made up by the city if it’s a “critical need.”

The city is facing the possibility of laying off one person from its five-person office of homeland security if the state goes ahead with its plan to cut 80 percent of Emergency Management Preparedness Grant funding for 2013.

New Orleans received $154,000 in 2012. It will get $49,368 this year if it goes through with the cuts.

In a March 4 letter to Kevin Davis, director of the Governor’s Office of Homeland Security and Emergency Preparedness, emergency preparedness directors from Orleans, St. Bernard, Plaquemines and Jefferson parishes wrote that the cuts could “significantly impact our ability to provide local emergency management.’’ Those directors demanded that the funding be restored.

“Also, there is a real fear that this decision could bring emergency management in Louisiana back to pre-Katrina level,” the emergency directors wrote.

Lt. Col. Jerry Sneed, New Orleans’ deputy mayor of homeland security and emergency preparedness, on Thursday said any cuts would hurt “badly” and said the money deserves to be spent locally since parish officials respond to local emergencies, not the state.

“If this is a critical need, New Orleans needs to make this a priority and fund it,” Davis said in a prepared statement his spokeswoman issued Thursday evening.

Sneed shot back on Friday, saying that even with its EMPG funds in 2012, 84 percent of the emergency management budget was funded by the city. The federal grant money the state gave the city, he said, went to pay a portion of the emergency managers’ salaries.

“We aren’t debating the need for GOHSEP, but the fact of the matter is GOHSEP serves parishes in a supporting role,” Sneed said. “It’s up to individual parishes to handle emergencies on the ground as they happen. This funding is critical.”

Now, Sneed said, GOHSEP is taking the money mid-year with “little explanation.”

“It’s going to have consequences all across the state,” Sneed added.