Rear Admiral Andrew Lewis, who heads the carrier strike group, said the vessel’s 65 aircraft would be used in the battle against the terrorist group.
‘We’ll spend the predominant part of our deployment in the Middle East,’ he said.
‘There’s a good chance that we’ll be flying missions over Iraq and Syria and executing the missions we are directed to do.
‘We’ve been at this kind of conflict for some time. They can be pretty difficult missions.
‘We’re doing things that we have been trained to do.’
The carrier dropped anchor off Stokes Bay on Sunday and will stay until Thursday.
Lieutenant Commander Reann Mammsen said virtually all of the carrier’s 5,000-plus company would have the chance to go ashore, providing a mini-boost for the local economy.
‘A lot of them will be going to London but a lot will be staying in Portsmouth,’ she said.
‘It depends on their schedules. Some have a couple of days and some just have a couple of hours.’
Among them will be Roosevelt’s commanding officer, Captain Daniel Grieco, who last visited the city with the navy 20 years ago.
‘It’s nice to come back,’ he said.
‘There are great people here. It’s a wonderful town. It’s a great place for my sailors to be able to go on liberty and enjoy themselves a bit.’
Portsmouth Naval Base commander Commodore Jeremy Rigby said it was a thrill to be hosting the carrier, one of 10 in the American fleet.
‘It’s brilliant,’ he said.
‘I used to serve on the USS Enterprise so I’ve got a feel for the scale of these. We’ve always prided ourselves on being a forward support for US forces going off to the east.’
Cdre Rigby said the visit whetted everyone’s appetite for the arrival of Britain’s new carrier, HMS Queen Elizabeth.
He said he hoped the new ship would be in Portsmouth by September 30 next year.
‘She will greatly improve our operations capacity and will give the United Kingdom a lot of influence on the world stage without having the commitment of boots on the ground,’ he said.
USS Theodore Roosevelt has just been through a four-year overhaul which saw her interior stripped and re-equipped with the latest technology. The ship’s crew members hail from right across the United States and even include a number of Royal Navy sailors on exchange programmes.
First Class Petty Officer David Frech, 37, of Ohio, said he was looking forward to going ashore and learning more about Britain’s history and culture.
He said: ‘I’m going to go and see parliament and Big Ben. I’m also going to explore around Portsmouth, and go on a tour to see Stonehenge, so really try to cover as much ground as possible.’
About two-thirds of the crew have never been to the UK before and many had never left the US before this mission.
Ensign James Nichols, from Virginia, said: ‘We’re looking forward to doing some touring and eating some good food.’