Defense Secretary Jim Mattis says the revamped U.S. strategy for Afghanistan, which he promised by mid-July, is still not finished.

Mattis, speaking to reporters in an impromptu session Friday, said "it's underway," but would not says how soon it will be ready to present to the president. "You know me, I don't give timelines," he said.

Even though it's already mid-July, Mattis said mid-July remains his goal to complete the review.

"Somewhere around there," he said. "We are driven by the maturity of the discussion, and where we're at. We're not going to meet some timeline if we are not ready, but we are pretty close."

One holdup appears to be a White House initiative backed by chief strategist Steve Bannon to use private contractors to train and equip Afghan forces in the future, a proposal that was first reported by the New York Times.

Mattis is said to be opposed to the idea, which is designed to save money but is often more expensive than using U.S. military personnel.

The idea of using more contractors and fewer troops was defended Thursday by Sebastian Gorka, presidential deputy assistant. He told CNN, "We open the door here at the White House to outside ideas."

"It's about saving the U.S. taxpayer money, it's about creating indigenous capacity," Gorka said. He also appeared to confirm that Erik Prince, a founder of the private security firm Blackwater Worldwide, was among those approached for alternatives to dispatching more U.S. troops.

"This is a former operator. This is a man who hires former operators, first tier, special operations forces, retired individuals, not to go and fight there instead of somebody else, but to help the Afghans, to help local indigenous forces protect their own territory," Gorka said. "So this is a cost-cutting venture."

This week, Sen. John McCain, R-Ariz., chairman of the Senate Armed Services Committee, expressed frustration that the promised strategy has not been provided to the Congress, and threatened to insert his own strategy into the Senate version of the National Defense Authorization Bill.

At a defense ministers meeting in Brussels last month, NATO countries committed to send several thousand additional military trainers to support the alliances "Resolute Support" mission of which the U.S. contribution was expected to number as many as 4,000 troops.