Britain has an obligation to take back “innocent” children born to Islamic State fighters in Syria, the defence secretary has said, arguing that the UK needs to resolve its failure to repatriate minors caught up in the Syrian civil war.

Penny Mordaunt said she wanted to “build up a very clear picture” of where children have been taken into camps as Syria’s violent conflict has subsided and be prepared to allow them to come to the UK.

Speaking at a military conference in Westminster, she said: “I think the British public would agree we absolutely have an obligation to innocents who were taken into a war zone.”

Mordaunt added: “Extracting them would be a very difficult thing to do and would in all practical honesty require the practical consent of the parents who were there.”

France and Germany have begun taking back children caught up in the conflict, while the International Committee of the Red Cross (ICRC) has said it would help repatriate children to the UK from the crowded refugee camps in north-east Syria.

There are estimated to be 76,000 women and children living in the al-Hawl refugee camp in Syria. A thousand of the children are unaccompanied and many are believed to be of European descent.

The issue was brought into sharp relief in February when Shamima Begum, then a British citizen, asked to be allowed to return from Syria with her infant son. Sajid Javid, the home secretary, responded by stripping her of British citizenship and the child died of pneumonia shortly after.

Jeremy Hunt, the foreign secretary, said in March that the UK would look at ways of bringing back British children with the help of Mordaunt’s previous ministry, the Department for International Development, but no progress has been made.

Mordaunt added that the question of how to deal with British Isis members and their children was being discussed by the UK’s National Security Council (NSC). An estimated 850 people left the UK to join Isis in Syria or Iraq, and a third are estimated to be alive in the region.

Regarding British fighters, Mordaunt said even if the UK did not want to take those people back and put them through the justice system, the country had to work with the international community to decide how to deal with them.

“We have spent collectively a lot of blood and treasure rounding up and detaining individuals, and to create a situation where they disappear or where they are moved to other nations would be a dereliction of our duty,” she said, adding: “We need to come up with answers for these very difficult problems, and that is the focus of the NSC.”

Mordaunt has been tipped as a possible Tory leadership contender, although it is not clear how much support she enjoys among Conservatives. When asked whether she was running, she would only say: “I think the focus this week should be on D-day veterans.”

The UK marks the 75th anniversary of the D-day landings on Thursday.