Gavin Williamson spoke amid a mounting diplomatic row with the US over the jihadis’ fate, with his American counterpart insisting terrorists' “countries of origin” must take responsibility.
Speaking in Brussels, Mr Williamson said Alexanda Kotey and El Shafee Elsheikh “have turned their back on British ideas, British values”.
“Do I want them back in the United Kingdom?” he asked. “No, I don't.”
The former Londoners are among hundreds of foreign fighters captured by the US-backed Syrian Democratic Forces (SDF) in advances that retook all of Isis’ major strongholds in Syria.
Jim Mattis, the US Secretary of Defence, previously said that “the important thing is that the countries of origin keep responsibility for them”.
He and Mr Williamson spoke on Wednesday morning but officials have not announced the results of their discussions.