Nearly 800,000 refugees in Africa have had their food rations slashed due to a lack of global aid funding, threatening to push many to the brink of starvation, the UN has said.

The cuts of up to 60% are "threatening to worsen already unacceptable levels of acute malnutrition, stunting and anaemia, particularly in children", the UN's World Food Programme and refugee agency, UNHCR, said.

The heads of the two agencies were in Geneva this week to make an urgent appeal to governments for more funds to help feed Africa's refugees. "It is unacceptable in today's world of plenty for refugees to face chronic hunger," said the UNHCR chief, António Guterres.

The WFP will need $186m (£108m) by the end of the year to restore full rations and prevent cuts, while UNHCR said it needed another $39m to fund the nutritional support it provides to vulnerable refugees across the continent.

"Many refugees in Africa depend on WFP food to stay alive and are now suffering because of a shortage of funding," the organisation's executive director, Ertharin Cousin, said.

Refugees hit by ration reductions were desperately looking for ways to put food on the table, with the crisis pushing increasing numbers of children to quit school to seek work and prompting families to marry off their girls at a younger age.

"Survival sex" prostitution by women and girls trying to raise money for food was also a growing concern, the agencies said.

The funding crisis has forced the WFP to cut rations for a third of the 2.4 million refugees it helps feed in 22 African countries, with more than half of the 800,000 affected seeing rations slashed by at least 50%.

The situation was most dire for the 300,000 refugees in Chad – mainly from Sudan's Darfur region and the Central African Republic – whose rations had been cut by as much as 60%, the statement said.

In many cases, refugees were left with rations of just 850 calories per day, compared with the recommended 2,100 calories adults should consume to remain healthy.

"Desperately hungry refugees continue to cross daily into southern Chad from the strife-torn Central African Republic, only to find that hunger does not stop at the border," the WFP and UNHCR said.

It cited the case of 24-year-old Habiba who walked with her four children for three months through the Central African bush to escape the violence ravaging the country, often going days without food and water.

Habiba – who gave birth to her youngest daughter along the way but who became so weak, starved and dehydrated she could not breastfeed – crossed into Chad, only to discover that UNHCR's Dosseye border camp had run out of supplementary food for pregnant and nursing mothers, the agencies said.

The situation was not much better for some 150,000 refugees in the Central African Republic or in South Sudan, where supplies had also been cut by at least half, while another 338,000 refugees in Liberia, Burkina Faso, Mozambique, Ghana, Mauritania and Uganda had seen their rations dwindle.

In addition, a series of unexpected, temporary ration reductions, sometimes owing to insecurity, had hit camps in several countries since early 2013, including Kenya, Ethiopia, Congo-Brazzaville, the Democratic Republic of the Congo and Cameroon.

"The number of crises around the world is far outpacing the level of funding for humanitarian operations, and vulnerable refugees in critical operations are falling through the cracks," Guterres said.

He warned that even small cuts to rations could spell disaster for already undernourished people, with the impact, especially on children, "immediate and often irreversible".