The British government has announced an emergency aid package for refugees fleeing violence in Ivory Coast amid concerns that the fighting could spread and destabilise west Africa.

The Department for International Development said it would provide £16m to humanitarian agencies to provide emergency aid to Ivory Coast and Liberia.

On Friday, the UNHCR, the UN's refugee agency, estimated that between 700,000 and 1 million people could now be displaced following Ivory Coast's disputed presidential election last November. More than 100,000 people are estimated to have crossed the border into Liberia, around 62,000 of them arriving between 24 February and the middle of last week.

"Most refugees are seeking safety in Nimba County [in Liberia]. However, since this week, we have been seeing many more cross into Grand Gedeh County, further south. On Tuesday alone, more than 6,000 Ivorians entered the region and settled in remote areas in and around Janzon, Tuzon and Sweaken, including in villages that are inaccessible by car. The new arrivals fled from Blolequin," said spokeswoman Melissa Fleming.

The news comes as Alassane Ouattara, the internationally recognised winner of last year's election, rejected the representative chosen by the African Union to negotiate a settlement to the presidential crisis with incumbent Laurent Gbagbo, further raising the prospect of civil war in the country.

Fleming said that as well as avoiding being caught in the crossfire, some people told the UN they were leaving their homes because they "can no longer cope financially due to closures of banks and businesses, and resulting unemployment. Costs of food have risen, and there is little available in the markets."

Last week the UN high commissioner for refugees, António Guterres, visited Liberia and warned that the influx of refugees threatened the country's eight years of peace, following a civil war that left up to 300,000 people dead and thousands more displaced.

"The amount of human suffering is horrendous. All neighbouring countries can be dramatically impacted," he said.

The Liberian president, Ellen Johnson-Sirleaf, has already expressed her concerns, telling Reuters: "We're already at war. We hope there will not be an escalation of war. It's a serious threat to the stability of Liberia, and I might say to the stability of all neighbouring countries."

IRIN news agency reported that some Ivorians have begun to head to Ghana. As of Saturday, 3,000 Ivorian refugees were understood to have been registered by immigration officers.

Aid agencies and NGOs are warning of a humanitarian disaster caused by the displacement.

Giuliano Vascotto, Save the Children's director of operations in Ivory Coast, said: "Violence is increasing in Abidjan and the west of the country, with more and more people fleeing their homes every day."

Oxfam warned that the situation could become Africa's forgotten crisis. Chals Wontewe, Oxfam's country director in Liberia, said: "Fighting is spreading across cities in Ivory Coast, and the risk of large-scale refugee flows is high. But despite the gravity of the situation, it is not getting the attention or funding it deserves.

"The border areas are dangerous, and living conditions there are desperately poor. There is an urgent need for transportation to help refugees move to camps further inside Liberia, where food and shelter can be safely provided. This needs to happen before both the rainy season and further refugee flows make the challenge even harder."

Meanwhile, a coalition of 32 international and African civil society groups, including Human Rights Watch, called for an increase in humanitarian aid, more peacekeepers and an inquiry to investigate post-election human rights violations.

The UN Central Emergency Response Fund (Cerf) has allocated $10.4m to seven agencies working in Ivory Coast to help meet the urgent humanitarian needs. In January, the UN Office for the Co-ordination of Humanitarian Affairs appealed for $32m to tackle the crisis, but has only received $7m.

The UK government said the £16m will provide food, shelter and basic services for 20,000 Ivorian refugees in camps and border villages in Liberia and for 25,000 men, women and children displaced in Ivory Coast. The aid will be channelled through the UN and NGOs.