But the counterterrorism effort the United States is undertaking with Iraq has its limits.

Iraq’s foreign minister has floated the idea of having American-operated, armed Predator or Reaper drones respond to the expanding militant network. But Mr. Maliki, who is positioning himself to run for a third term as prime minister and who is sensitive to nationalist sentiment at home, has not formally requested such intervention.

The idea of carrying out such drone attacks, which might prompt the question of whether the Obama administration succeeded in bringing the Iraq war to what the president has called a “responsible end,” also appears to have no support in the White House.

“We have not received a formal request for U.S.-operated armed drones operating over Iraq, nor are we planning to divert armed I.S.R. over Iraq,” said Bernadette Meehan, a spokeswoman for the National Security Council, referring to intelligence, surveillance and reconnaissance missions. For now, the new lethal aid from the United States, which Iraq is buying, includes a shipment of 75 Hellfire missiles, delivered to Iraq last week. The weapons are strapped beneath the wings of small Cessna turboprop planes, and fired at militant camps with the C.I.A. secretly providing targeting assistance.

In addition, 10 ScanEagle reconnaissance drones are expected to be delivered to Iraq by March. They are smaller cousins of the larger, more capable Predators that used to fly over Iraq.

American intelligence and counterterrorism officials say they have effectively mapped the locations and origins of the Qaeda network in Iraq and are sharing this information with the Iraqis.

Administration officials said the aid was significant because the Iraqis had virtually run out of Hellfire missiles. The Iraqi military, with no air force to speak of and limited reconnaissance of its own, has a very limited ability to locate and quickly strike Qaeda militants as they maneuver in western and northern Iraq. The combination of American-supplied Hellfire air-to-ground missiles, tactical drones and intelligence, supplied by the United States, is intended to augment that limited Iraqi ability.

The Obama administration has given three sensor-laden Aerostat balloons to the Iraqi government, provided three additional reconnaissance helicopters to the Iraqi military and is planning to send 48 Raven reconnaissance drones before the end of 2014. And the United States is planning to deliver next fall the first of the F-16 fighters Iraq has bought.