The United Nations says it has received just $22m (£14m) of the $415m it has appealed for in Nepal following the recent earthquake, and has called for aid contributions to be “dramatically ramped up”.

Jamie McGoldrick, the UN resident coordinator for Nepal, warned of a race against time to deliver relief supplies to remote areas – some of which are accessible only on foot – before the expected arrival of heavy monsoon rains next month.

Thousands have been affected by the devastating 25 April quake, and more than 7,800 killed.

“Of the requested $415m to support immediate humanitarian interventions, only $22.4m was received. This needs to be dramatically ramped up,” McGoldrick told reporters in the Nepalese capital, Kathmandu.

“The relief needs remain great and we urgently need funds to be able to continue our work.

“We need to [deliver relief] urgently, so that people have roofs over their heads and their other urgent needs are addressed before the monsoon season starts,” he said.

The 7.8-magnitude quake ripped through vast swaths of the impoverished Himalayan nation in Nepal’s deadliest disaster in 80 years. It destroyed close to 300,000 homes and injured almost 16,000 people. More than 100 were killed in India and China.

Paul Dillon, a project manager at the International Organization for Migration, urged the international community to dig deep.

“Someone has to open the tap,” he told reporters in Kathmandu on Friday. “We cannot run our responses on credit cards. Those who have offered help need to make good on their pledges.”