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Aid agencies have promised to stay in Afghanistan to meet humanitarian needs despite the Taliban seizing control of the country.
But they issued a warning that there was too little funding to address the crisis and that governments needed to intervene to protect aid workers.
UK Defence Secretary Ben Wallace said on Monday that Britain may need to co-operate with the Taliban to ensure humanitarian aid.
Save the Children, which said 120,000 children had been displaced since June, said it was “committed to staying and providing support to those most in need”.
Aid workers at the charity have been “delivering life-saving services to communities in Taliban-held or contested areas for seven years”, it said.
The medical assistance group Doctors Without Borders (MSF) said it was moving patients to a newly-opened trauma centre in Kunduz.
The new centre will have an emergency room, operating theatres and an intensive care unit.
MSF said it was continuing to provide medical services at all five of its centres in Afghanistan and had set up an emergency trauma unit at a field office.
The displacement of more than 500,000 people during the fighting in Afghanistan has prompted fears of a refugee crisis.
The UN’s refugee body, UNHCR, said it would “stay and deliver for the Afghan people as long as we have access to populations in need”.
Another UN body, Unicef, already has a working relationship with the Taliban after persuading the group to approve the establishment of 4,000 informal schools last year.
UN Secretary General Antonio Guterres urged the Taliban to ensure that humanitarian workers had access to the country.
The UN “remains determined [to] provide life-saving humanitarian assistance and critical support to civilians in need,” Mr Guterres’s office said.
The UN’s humanitarian body, OCHA, said assessment teams had not been operating on Sunday afternoon as the Taliban overran the capital.
Health workers were helping displaced people and more assistance was on the way for people forced out of their homes, the agency said.
The International Rescue Committee, an NGO, said Afghans were “entitled to aid based on their needs, not whose control they live under”.
But it said that humanitarian assistance efforts only had 38 per cent of the funding that they required.
The IRC called on Washington to “use its diplomatic muscle” to bring about a ceasefire and ensure that aid workers could safely operate in Afghanistan.
“Humanitarians like the IRC have remained in Afghanistan through crisis after crisis,” said senior director Amanda Catanzano.
“But we urgently need the financial and diplomatic support of the international community to do so effectively, securely, and without legal risk.”
The Mercy Corps, which helps to provide clean water and sanitation supplies in Afghanistan, said it would stay in Kabul “as long as we safely can”.
“It’s happening so rapidly we don’t yet know the full scale of the situation or what the coming days and weeks will bring beyond more displacement and chaos,” said Ram Krishan, a Mercy Corps director in Kabul.
After withdrawing their troops from Afghanistan, Nato countries are now evacuating civilians from Kabul’s airport.
UK Prime Minister Boris Johnson said countries should not unilaterally recognise the Taliban as the government of Afghanistan.
But Mr Wallace acknowledged that some dealings with the militants would be necessary to provide humanitarian aid.
“We have our ambassador in the country. One of the jobs of our ambassadors is to reach out to whatever the government is,” he told BBC television.
“We need aid – what we know is failed states lead to terrorism and lead to poverty, and we need to therefore ensure we have pathways for aid.”