Boris Johnson and other world leaders have received assurances from the Taliban that foreign nationals and those with authorisation to flee Afghanistan will be free to leave as tensions and bloodshed escalate on the streets of Kabul.

On Sunday US forces launched a military strike against a vehicle said to be carrying “multiple suicide bombers” from Islamic State’s local affiliate who were planning to attack Kabul airport. According to some reports, a child died in a second blast.

A significant number of British citizens told the Guardian they continued to wait at the airport in the hope of being rescued despite the terror threats and the departure of all UK troops at the weekend. They sent video footage of several clasping UK passports and pleading for help. Desperate Afghans have been told to cross the border into neighbouring countries to escape the Taliban takeover.

On Monday, the UN security council is expected to discuss the Taliban’s reassurances – revealed in a statement on Sunday evening – following deepening concerns over the plight of thousands of Afghans with western links who are at their mercy.

France and Britain were expected to table an emergency UN security council resolution calling for any new Afghan government to back a safe zone at Kabul airport to allow evacuation efforts to continue, Emmanuel Macron said, though a Whitehall source claimed the French president’s comments were “premature”.

In a joint statement released on Sunday by the UK government along with the United States and more than 90 other countries, it was confirmed that the Taliban had said anyone who wished to leave the country could do so – though the regime’s pledges will be greeted with scepticism.

The joint statement said: “We have received assurances from the Taliban that all foreign nationals and any Afghan citizen with travel authorisation from our countries will be allowed to proceed in a safe and orderly manner to points of departure and travel outside the country.”

Last week, the Taliban caused shockwaves by moving to prevent Afghans from leaving the country, declaring the route to Kabul airport open only to foreigners. Western forces have been trying to evacuate Afghans who have supported foreign operations as they fear they and their families could be tortured and murdered for working with western powers during the 20-year war.

The Taliban’s latest assurances are part of delicate negotiations as the new regime seeks to work with foreign governments. Johnson said on Sunday that if the regime wanted diplomatic recognition and aid funding, they would have to ensure “safe passage” for those who want to leave.

In a further development, Britain is being urged to spearhead an international plea for “hard cash” to fund refugee camps in countries bordering Afghanistan. John Healey, the shadow defence secretary, said ministers have failed to involve critical partners in the region to avoid the current crisis despite knowing for months that the withdrawal would happen this year.

“Britain must lead international efforts to get neighbouring countries to set up safe haven camps. There has to be hard cash on the table to fund safe haven camps and the countries willing to take them.”

It comes after 15,000 people were evacuated from Afghanistan by UK troops over the course of nearly two weeks under Operation Pitting, believed to be the largest evacuation mission since the second world war.

Whitehall sources believe that up to 9,000 others with links to the UK government could be left behind, however. Those remaining will be expected to reach a third country such as Pakistan, Uzbekistan or Tajikistan in order to be resettled in Britain.