Haltemprice and Howden MP Mr Davis told the Commons that three of the estimated 60 British children thought to be in the region are orphans, adding that those who have not been orphaned "still deserve the United Kingdom's protection".
He argued that many are aged under five and "should not be punished for their parents' mistakes", before adding that some of the UK's international allies have used a ceasefire to repatriate their own children.
Asking an urgent question in the Commons yesterday, Mr Davis said: "If we do not do the same, British children will be left at the whim of a brutal dictator or a terrorist organisation or roving bands of militia.
"If we do nothing, we'll be abandoning our moral obligations and risking those vulnerable children to growing up in a war-torn area and maybe turning into terrorists themselves.
"The time to act, minister, is now."
Foreign Office minister Andrew Murrison said the UK's approach is informed by "compassion and care" for individual cases, adding the priority was unaccompanied children and orphans.
He said he did not recognise the figure of 60 mentioned by Mr Davis, but said the UK is talking to agencies in order to "better understand the situation".
Mr Murrison added: "Of course we will do all we can."
He said accessing camps and people is "extremely difficult" and outlined a hope that the ceasefire in north-east Syria will be sustained, adding: "Under those circumstances, of course, all things become possible."
Shadow Foreign Secretary Emily Thornberry said the Government should consider repatriating British mothers who travelled to Syria to face justice in the UK, if that is what is best for their children.
She added: "It is all very well for some to say that 'the sins of the father, and in many cases the mother, should be visited on the children'. But that is not who we are as a country or a people.
"Instead, I believe we have a moral duty and a civic duty to ensure that these British children are brought back to the UK to receive shelter, care and the counselling that they need.
"Even if that necessitates bringing back their mothers to face justice in our courts, for the crimes that they may have committed."
Responding, Mr Murrison said: "These are innocent minors. They are vulnerable people and we must do what we can for them.
"It is entirely wrong to associate them with what their parents may have done."
Former Foreign Office minister Alistair Burt said: "It has seemed to me over a period of time that we have to recognise an international responsibility to take back even those who have been indoctrinated and radicalised in order to protect the children."
The Independent MP for North East Bedfordshire added: "We should have the resources in order to be able to deal with them as well as to protect the children who are the only innocents by and large in this situation."
Responding, Mr Murrison said the Government is trying to identify British children in refugee camps, adding: "In particular, trying to enumerate those who might be considered to be vulnerable in this piece.
"What I said earlier is we are approaching this on a case by case basis. Genuinely that is the case, it is not easy because our access is obviously imperfect.
"I hope very much that if this ceasefire holds, then we will be able to do more than perhaps we have been able to do up to this point."