OTTAWA - When Brig.-Gen. Greg Smith first touched down in Iraq in February to advise and assist the Iraqi army in its fight against Islamic State militants, he assumed that ISIL had the upper hand.

Instead, what he found - amidst the grit and violence and destruction that has consumed large chunks of Iraq and neighboring Syria - was an Iraqi army that would not back down.

"They are crushing them in many ways and pushing them back," said Smith, the Canadian chief of staff of the Combined Joint Forces Land Component Command for Operation Inherent Resolve, the American-led coalition whose mission is to help guide Iraq's own forces.

In his first media interview since deploying to Iraq, Smith said he had underestimated the prowess of the Iraqi soldiers.

Much of the Iraq army had collapsed and fled when the Islamic State of Iraq and the Levant - variously known as ISIL, ISIS or Daesh - swept through swaths of Iraq in 2014, capturing its second-largest city, Mosul.

And yet when he arrived, it was the militants of ISIL who were on the run, Smith said.

"I have to admit I was very surprised to see how badly they were doing once I got here and started getting read in on operations," he said.

"The Iraqi forces, notwithstanding perhaps somewhat of a poor brand based on how activities occurred in 2014, are quite honestly taking it to Daesh."

Smith said he was "minding my business" as commandant of the Canadian Army Command and Staff College in Kingston, Ont., when "my boss called me one day and said, 'Hey, you're promoted and going to Iraq."'

He arrived shortly before Iraq announced the beginning of an offensive to retake Mosul by the end of this year.

Since then, Iraqi forces have been attacking northward toward the city along the Tigris River. They are supported by coalition airstrikes and, on the ground, by some 200 U.S. Marines providing indirect artillery support from a base near the town of Makhmour. One Marine was killed in an Islamic State rocket strike in March.

Make no mistake, though: the campaign to capture Mosul will be long and difficult, Smith warned.

"Even if this was the Canadian army trying to do it, this would be a tough fight," he said in a phone interview from Baghdad.

"But we're training with the Iraqis right now. We're doing that 'building partnership' piece. 1/8 The Iraqis 3/8 have begun operations to isolate that part of their forward line of troops. And I'm actually quite impressed with their tactical agility and their speed."

All of the military operations are planned and led by Iraqis, he pointed out. "This is not a coalition effort. This is us supporting the Iraqi government and the Iraqi forces. We support them with operational fires. We provide surveillance for them. We provide advise-and-assist (support)."

Targets for coalition airstrikes are chosen in consultation with the Iraqis, he added.

"We have joint targeting cells. Every one of those targets are approved by the Iraqi army, or if it's up in the north, it's potentially by Kurdish forces. That is done hand-in-hand. If the Iraqis or the Kurds say don't hit that target, that's not what we do."

Based in Baghdad, Smith is one of three one-star Canadian generals assigned to Operation Inherent Resolve.

Brig.-Gen. David Anderson leads a team that liaises with Iraq's defence and security ministries, a job Smith compared to that of the "strategic advisory team" Canada sent to support the Afghan government. Brig.-Gen James Irvine, based in Kuwait, is commander of Canada's Joint Task Force-Iraq, which includes all Canadians involved in the mission. He will be replaced today by Brig.-Gen. Shane Brennan.

While Smith's team works mainly with Iraqi regular forces, Canadian special forces are training and advising Kurdish peshmerga fighters in northern Iraq, where the Kurds are holding a line east and north of Mosul. It's an active front that ISIL often attacks.

Smith says Canadian special forces in the area, who are officially in a non-combat training role, sometimes work "from the forward line of troops." They have exchanged fire with the enemy. One Canadian soldier, Sgt. Andrew Doiron, died last year in a friendly-fire incident near the front.

The Kurds, however, are unlikely to take part in any direct assault on Mosul. The city lies beyond land they consider Kurdish territory. Most peshmerga, when asked, will say they are fighting for Kurdistan rather than a united Iraq.

That presents complications for Iraq's international partners.

"We are here supporting Iraq," said Smith. "This is a one-country policy from a Canadian perspective and from a coalition perspective. I've seen on the news plans for Kurdish separation, or whatever. I've heard 1/8 peshmerga and Iraqi regular forces 3/8 tactically work very well together. It's a respectful relationship. We're enabling both sides.

"As for the longer political solution, that is very much an Iraqi democratic problem."