Theresa May has declined to make any extra commitments on receiving child refugees affected by the demolition of the Calais refugee camp, after the French president, François Hollande, rang her to ask for the Britain to consider its “moral duty”.

Downing Street said the UK has already taken a “considerable number of unaccompanied minors”, and several hundred more children and young people would be arriving in the coming weeks.

The government has taken about 274 child refugees this month, mostly those with family ties to the UK under the Dublin regulation. David Cameron also promised earlier this year to take an unspecified number of vulnerable child refugees from France, Greece and Italy after coming under pressure to accept an amendment to the law from the Labour peer Alfred Dubs, who was rescued in the second world war Kindertransport evacuation.

But May is still facing calls from French politicians, some British MPs and charities to speed up its processes and take more unaccompanied minors who had been living in the Calais camp but are now being transferred across France.

Hollande revealed on Saturday that he had pressed May to take Britain’s fair share of the 1,500 asylum-seeking children left in Calais who are due to be been dispersed to reception centres throughout his country.

He spoke to May to ensure that British officials would “accompany these minors to these centres and would play their part in subsequently welcoming them to the United Kingdom”.

“Their transfer to Britain is urgent,” he added. “We ask you to take your responsibilities and assume your moral duty by immediately organising their arrival.”

It is understood the phone call between Hollande and May centred on practical steps required to process the children’s claims after they have been relocated to specialist reception centres.

But sources said the prime minister did not make any new commitments to France that the UK would take in more child refugees, saying it was already taking action in accordance with the Dublin regulation and Dubs amendment.

A No 10 spokesman said:“We are firmly committed to working with the French to safeguard and protect children who remain in Calais – and that includes transferring eligible children to the UK safely and as soon as possible.

“We have already transferred a considerable number of unaccompanied minors to the UK so far this year, and as the home secretary told parliament this week, several hundred more children and young people will be brought to the UK in the coming days and weeks.”

Migrants arrive to attend the final service at a makeshift church in what remains of the Calais camp. Photograph: Thibault Camus/AP

The dismantling of the Calais camp began last week and is expected to be complete by the end of Monday.

A final service at a makeshift church in the camp took place on Sunday, attended by a small number of refugees and migrants who have not been transferred to reception centres across France.

By the weekend, around 5,000 people had so far been evacuated. A 1,500 remaining unaccompanied minors were housed in a camp made from shipping containers, before they are transferred to reception centres around France.

The announcement dismayed charities, which warned the dispersal policy could mean that many children might attempt to run away from the authorities out of fear.

UK Home Office officials had expected to process the children’s applications in Calais. However, a source told the Guardian on Saturday that “the French have pulled the plug” on the scheme.