By Aaron Ross

KINSHASA (Reuters) - Authorities from the Democratic Republic of Congo have issued an ultimatum to the country's U.N. peacekeeping mission to deport South Sudanese rebels rescued by U.N. forces, the mission (MONUSCO) said on Wednesday.

Opposition leader Riek Machar and more than 750 supporters fled into Congo in August following fierce fighting in the South Sudan capital of Juba. They were evacuated by MONUSCO from notheastern Congo to receive medical care and most are being held on three U.N. bases in eastern Congo, the mission said.

"There was an official document that was submitted to the Special Representative of the Secretary General setting an ultimatum, in a general manner, for the departure of these troops," spokesman Felix Basse told reporters in the Congolese capital of Kinshasa.

"They must leave Congo -- everyone knows that," he said.

He did not specify when the ultimatum expires, adding that talks were continuing with the Congolese and South Sudanese governments as well as regional organizations to find a solution.

However, no third country has yet stepped up to take them in, raising fears that the situation could threaten regional stability.

The influx of rebel fighters from volatile neighbors is a sensitive theme in Congo, where the flow of Hutu militiamen from neighboring Rwanda after its 1994 genocide helped trigger years of regional conflict in eastern Congo that killed millions.

Government spokesman Lambert Mende said the government has decided that the South Sudanese must leave Congo but declined to provide additional details on the government's ultimatum.

The spokesman for Machar's rebel force, the SPLM-IO, said on Tuesday that it was prepared to receive those that had fled back in South Sudanese territory that it claims to control.

"We have hundreds of our military personnel on (our) side of the Congolese border. We want the U.N. to transport them to our controlled areas," James Gatdet Dak told Reuters from Nairobi.

South Sudan's government applauded Democratic Republic of Congo's ultimatum.

"We would like to warmly welcome and appreciate the government of (Congo) for the wise decision to expel the remnants of Riek Machar from their soil," deputy government spokesman Akol Paul Kordi told Reuters.

Hundreds have been killed in battles that broke out in the world's youngest nation in July between troops loyal to Machar and President Salva Kiir, his long-time political foe. More than 20,000 South Sudanese refugees have crossed into Congo this year, according to the U.N. Refugee Agency.

(Additional reporting by Denis Duomo in Juba; editing by Ralph Boulton)