Maj Gen Patrick Roberson, commander of US special ops, also called on the government to repatriate two Londoners who have been called the “IS Beatles”.
The UK says El Shafee Elsheikh and Alexanda Kotey have been stripped of their British citizenship.
The government is negotiating for them to face trial in the US.
Speaking to the BBC from a jail in Syria in August, Mr Elsheikh and Mr Kotey disputed the claim that they had been stripped of their British citizenship.
Asked whether Mr Elsheik and Mr Kotey should be repatriated to the UK, Gen Roberson told the BBC: “We would certainly like them to be.”
He said the Syrian Democratic Forces (SDF) and the US were “working very hard to make sure that the countries of origin get these foreign terrorist fighters back into their custody”.
So far only a handful have done that.
Gen Roberson admitted it was a decision for each country involved, but he added: “I think the SDF and us would certainly like them to be repatriated to where they came from.”
He is the first senior US military officer to publicly call on the UK to take back its nationals and former nationals.
US-backed Syrian Democratic Forces say they have captured 700 foreign fighters from more than 40 nations, including the UK.
The SDF has not said how many are British – or former British nationals – but it is believed to be fewer than a dozen.
Mr Elsheikh and Mr Kotey, who were captured in January, are believed to be part of an IS cell which became known as “the Beatles’ by their hostages because of their UK accents.
The two men were associated with another Briton, Mohammed Emwazi – also known as “Jihadi John”.
He was seen in a number of high profile IS execution videos that showed the beheading of Western hostages, including US and British citizens.
Emwazi was killed in a US drone strike in Raqqa, Syria, in 2015.
The UK government has been in discussions with officials in Washington about sending the pair to the US to stand trial over their alleged involvement in the killing of a number of hostages.
If found guilty, they could face the death penalty.
Both men have questioned whether they could be stripped of their citizenship and tried in the US.
The comments of Gen Roberson suggest the US would prefer them to stand trial in the UK.
The mother of Mr Elsheikh has begun a legal challenge against the British government.
At a hearing at the High Court earlier this month, lawyers for the government confirmed that Mr Elsheikh had been stripped of his UK nationality in December 2014.
They have argued that there is insufficient evidence to prosecute him in the UK.
Mr Elsheikh’s mother is challenging Home Secretary Sajid Javid’s decision to share evidence with US authorities without seeking assurances the men would not face execution if they were extradited and tried there.