The situation in Kinshasa is already tense, with rioting on Tuesday in which Bemba supporters attacked the supreme court.
Kabila beat Bemba in a presidential election run-off on October 29. Bemba disputes the result, and his supporters and soldiers have been fighting Kabila's forces in Kinshasa.
A spokesman for Bemba, who served as vice-president in Kabila's transitional government, said he was unaware of any ultimatum.
Fidel Babala said: "He is still vice-president and is therefore allowed to keep a bodyguard."
The supreme court was set on fire after it began an assessment of a legal challenge brought by Bemba. Bemba alleges there was vote fraud.
Furniture and documents burned inside the court, and UN soldiers evacuated people who were inside.
The unrest started when police fired tear gas at a crowd of 200 Bemba supporters.
The fire followed violence earlier in the day, when pro-Bemba protesters retreated from police towards Bemba's official residence. Bemba's security guards fired at the police, witnesses said.
The shooting lasted for nearly an hour. About 100 judges, lawyers and journalists were trapped inside the court.
United Nations peacekeepers, who had tanks positioned outside, did not immediately intervene and some left the area. Many of the police officers also fled.
When the UN forces returned, about 50 of Bemba's supporters began throwing stones. They threatened to burn the court down and began looting its offices.
The peacekeepers fired machine-gun rounds into the air to disperse them. There was no immediate news of casualties.
The hearing was suspended after Bemba's lawyers protested at the composition of the legal panel. Kalonda Kele, the presiding judge, said: "We can't work in this climate of insecurity."
Bemba, one of DR Congo's four vice-presidents, formally contested the outcome of the election vote on Saturday after the Independent Electoral Commission (CEI) announced a win for Kabila, the country's incumbent president.
The supreme court then had seven days to rule on the challenge to the results, which gave Kabila just over 58 per cent of the vote, compared to Bemba's 42 per cent.