The NATO alliance says it is considering getting more involved in efforts to combat the Islamic State extremist group.

Secretary-General Jens Stoltenberg says NATO defense ministers on Wednesday ordered the alliance to draft a proposal for training the Iraqi military inside Iraq, and helping build its capacity.

NATO brass will also advise how alliance AWACS surveillance aircraft could help the U.S.-led anti-Islamic State coalition by monitoring Syrian and Iraqi airspace.

U.S. Defense Secretary Ash Carter welcomed the development, but said it should go further.

Following a meeting of NATO defense ministers in Brussels, Carter said he'd "like to see NATO do more."

As examples, he cited NATO's proven ability to assemble a multinational military force and integrate contributions from smaller countries in a collective effort.