WASHINGTON — A proposal to send National Guard troops to the U.S.-Mexico border to counter drug trafficking has triggered a bureaucratic standoff between the Pentagon and Department of Homeland Security over the military's role in domestic affairs, according to officials in both departments.

The debate has engaged a pair of powerful personalities, Homeland Security Secretary Janet Napolitano and Defense Secretary Robert Gates, in what their subordinates describe as a turf fight over who should direct the use of troops to assist in the fight against Mexican cartels and who should pay for them.

At issue is a proposal to send 1,500 additional troops to the border to analyze intelligence and to provide air support and technical assistance to border agencies. The governors of Texas, Arizona, California and New Mexico made the request in January, drawing support from Napolitano but prompting objections from the Pentagon, where officials argue that it could lead to a permanent, expanded mission for the military.

President Barack Obama has signaled that he is open to the idea, asking Congress for $250 million to deploy the National Guard while also saying he was "not interested in militarizing the border." The issue, which has been stalled before a National Security Council policy committee, will be decided by the president.

Neither Napolitano nor Gates has made the disagreement personal, although some of their aides have privately expressed exasperation at what one called an interagency "food fight."

"It should not be that we always rely on the Department of Defense to fulfill some need," said Gen. Victor E. Renuart Jr., head of the U.S. Northern Command, which is responsible for defending the continental United States. Border law enforcement agencies should have adequate funds to do their job, he said. If the Guard is tapped, it should be for capabilities "that do not exist elsewhere in government," Renuart said. "When we send the National Guard, they go with specific missions, with specific purposes. And we put some duration on that so there is an end state."

Homeland security officials and governors counter that there is a legitimate need for troops to back up border agencies against the most serious threat to the Southwest and that a deployment would not represent a new military mission. Under a 1989 law, the National Guard already assigns 577 troops to help states with anti-drug programs that "can easily expand," the four governors wrote Congress in April.

Napolitano, who as governor of Arizona prompted President George W. Bush to send 6,000 National Guard troops to the border in 2006, has supported the governors.