CALGARY - The soldier who oversees U.S. forces in Afghanistan is giving Canada's top soldier an operational briefing while on what is described as a social visit to the Calgary Stampede.

In this case, R and R stands for rest and reconaissance.

Gen. David Petraeus, the head of U.S. Central Command, is best known for co-ordinating the troop surge in Iraq that is credited with significantly reducing violence there.

He took responsibility late last year for American forces in Afghanistan.

His visit to Calgary comes as nearly 4,000 U.S. marines and 650 Afghan troops launched a massive offensive in Helmand province -- the opening phase of U.S. President Barack Obama's new strategy in Afghanistan

He was invited to Calgary by Gen. Walter Natynczyk, who took over last year as Canada's Chief of Defence Staff.

"We are going to sit down and talk obviously about all that's going on in Central Command area of responsibility, which includes Afghanistan, Pakistan, Iraq and a host of other places," Petraeus said in an interview with The Canadian Press.

"There's a lot going on out there and we'll compare notes on all that but obviously, we're also here for the Stampede. It's great being one of those wearing a white hat," he chuckled.

Calgary Mayor Dave Bronconnier presented Petraeus with a white Smithbilt cowboy hat, a traditional honour for dignitaries and special guests to the city.

The surge in American troops in Helmand province is impressive, considering Canada has only 2,700 troops in the entire country, primarily in the Taliban stronghold of Kandahar.

Kandahar will be the next area targeted, the U.S. general said.

"Helmand is a very substantial operation. It is part of the operations which deploy the additional forces which have been deployed to Afghanistan and of course more are on the way," Petraeus said.

"By early fall we will have more than doubled the U.S. forces on the ground -- we'll be at 68,000 total. At that point of time some of those that will be dispatched will be going into the Kandahar area where they will work very closely with the Canadian forces."

During the white hat ceremony the U.S. general paid tribute to the soldiers fighting alongside the Americans in the war-torn country.

"It's a privilege to do the job that I do and it's a particular privilege to do it with great troopers from a lot of different nations and the people of Canada foremost among them," he said.

"It's a pleasure to accept this honour and for the soldiers and marines that are out there in the Central Command area."

Natynczyk worked with Petraeus in Iraq in 2004 and received his own white hat last year.

"Thank you for allowing show our gratitude for your leadership, enabling the success of our men and women who are deployed shoulder to shoulder," he said.

The two officers plan to watch the Calgary Stampede parade Friday morning and visit Afghanistan360, a multimedia exhibit on Canada's civilian and military efforts in Afghanistan.

The exhibit features stories from the field and short video segments on training and development projects that Canada supports in Afghanistan. Visitors can record 15-second video messages to troops serving in Afghanistan.

Since the mission began in 2002, 120 Canadian soldiers have died in Afghanistan.

Petraeus, who seemed at a bit of a loss after receiving and reluctantly putting on the hat, said he has a better idea of what the Calgary Stampede is now.

"As we came in here I was trying to get some sense about what this whole thing is all about. Our driver was from the Canadian army and I asked if this was sort of the Super Bowl of rodeos and he said, 'No sir, this is the Stanley Cup of rodeos."'