Gavin Williamson said that Britons who had gone to Syria or Iraq to fight for ISIS hated what Britain stands for, and that air strikes could be used against the estimated 270 British citizens who are still out there.
"Quite simply my view is a dead terrorist can't cause any harm to Britain," Williamson told the Daily Mail in an interview published late on Wednesday.
"We should do everything we can do to destroy and eliminate that threat," he said, adding that he believed any British fighters who joined ISIS should never be allowed to return to the United Kingdom.
Williamson, 41, has been defence minister for little over a month, replacing Michael Fallon after he quit in a sexual harassment scandal.
After the death of Jones, who was known as the "White Widow", Fallon said that British nationals who chose to leave the UK and fight for ISIS were a "legitimate target".
(Reporting by Alistair Smout)