By Stephanie Nebehay

GENEVA (Reuters) - More than half a million people in northern Mali, occupied by Islamist fighters, need aid to cope with rising food prices, collapsed public services and a lack of health care, the International Committee of the Red Cross said on Thursday.

The independent agency said it is in regular contact with the militants to facilitate its aid deliveries in the north and has raised the issue of amputations carried out in what rebels say is the application of Islamic sharia law.

"The (humanitarian) situation is more and more alarming for the population, both the displaced and residents who have stayed put," Yasmine Praz Dessimoz, head of ICRC operations for North and West Africa, told a news conference in Geneva.

Mali was plunged into chaos in March when soldiers toppled the president, leaving a power vacuum that enabled Tuareg rebels from the north to seize nearly two thirds of the country.

The Tuareg rebellion has since been hijacked by Islamist militants who have began imposing sharia, Islamic law, in the northern regions of Gao, Kidal and Timbuktu under their control.

"Public services practically no longer function, basic health services are not provided and supplying clean drinking water is difficult. Needs are huge," Praz Dessimoz said.

Gao hospital, the largest in northern Mali with 160 beds, lacks medicines and personnel after many healthcare workers fled to the south and there are few goods at the markets in the north, she added.

Islamist fighters cut the hands and feet off five suspected robbers in the northern city of Gao, residents and a hospital official said on Monday.

"Amputations have taken place ... It is important to have a humanitarian dialogue with the different groups there regarding this assault on the physical integrity of people," Praz Dessimoz said. "The message has been transmitted, that's clear."

The ICRC, which deploys 111 aid workers in Mali, is one of few humanitarian organizations to have access to all of northern Mali, where no United Nations aid agencies deploy any staff.

"It is through concrete actions and our distributions that we manage to gain our acceptance and continue to work. Our dialogue allows us access and the ability to distribute aid," Praz Dessimoz said.

"Today there is not so much fighting, small outbreaks of violence here and there in different urban zones, but it has calmed down greatly," she said.

The ICRC distributed food rations to 160,000 needy people in the north during July and August and aims to reach a further 360,000 in the north, as well as 60,000 northerners who fled to Mopti in the south.

The total of 580,000 is about one quarter of northern Mali's population before the hostilities, Praz Dessimoz said.

The ICRC appealed to donors for a further 25 million Swiss francs ($26.65 million), bringing its annual budget to 60 million francs for Mali, now its fourth biggest worldwide in budgetary terms.

Some 260,000 Malians fleeing the violence crossed into neighboring countries so far this year - Burkina Faso, Niger and Mauritania - according to the U.N. refugee agency UNHCR.

(Reporting by Stephanie Nebehay; Editing by Robin Pomeroy)