The rebel leader Laurent Kabila has agreed to extend for an unspecified period his deadline which had initially been set for today. If the UN fails to respond to his demand, he says his forces will have no option but to attack the camp, many of whose residents are suffering from hunger and disease.
Mr Kabila, who leads the Alliance of Democratic Forces for the Liberation of Congo-Zaire (ADFL), issued the demand after it was revealed that arms had been flown into the camp.
The Zairean government, which since last October has been desperately trying to halt the rebel advance, is the principal suspect in the supply of arms to Tingi Tingi.
UN Secretary General Kofi Annan, who has confirmed the illegal delivery of arms to the camp, has sent a special envoy, Mohammed Sahnoun, to negotiate with the Zairean government in the capital, Kinshasa.
The UN High Commissioner for Refugees, Sadako Ogata, who recently visited Tingi Tingi, has repeatedly appealed to Mr Kabila to allow the camp's residents to return safely to their native Rwanda.
Having conceded that there is a problem with extremists living alongside the refugees, Mrs Ogata said last week that she had no solution for separating the two groups.
The Zairean government, which denies the charges of supplying arms to the camp, has been fighting a losing battle against the rebels who now control most of eastern Zaire. Kinshasa has been recruiting foreign mercenaries and exiled Rwandan extremists to bolster its own flagging army.
Tingi Tingi lies directly in the path of the rebels who are committed to the overthrow of Zairean president, Mobutu Sese Seko. It is one of the last strongholds in Zaire for refugees from Rwanda's Hutu majority who fled their country following the 1994 genocide of at least half a million Tutsis and moderate Hutus.
Among the refugees who settled in eastern Zaire were many Hutu extremists responsible for the genocide. When late last year the rebels drove hundreds of thousands of Rwandan refugees out of their camps in eastern Zaire, many militants were among the tide of humanity which poured back into Rwanda.
Countless exiled Hutu fighters and extremists, however, turned westwards into the Zairean rainforest. Thousands of innocent refugees were forced to flee with them as cover. Hemmed in by the conflict between the Zairean army and the ADFL rebels, they settled with their families in Tingi Tingi and other encampments.
"The refugees are not our enemy," says Raphael Ghenda, ADFL Commissioner for Information. "These people have been taken hostage by members of the former Rwandan army and militants who are killers.
"They are being used as a human shield. We have asked the international community to disarm these killers and remove them from the camp. If this is not done we'll have to find our own solution."
Speaking in the eastern Zairean city of Goma, headquarters of the ADFL, Mr Ghenda admitted that there was a danger of innocent people losing their lives if an attack was launched on the camp. However, he insisted the ADFL had no choice. He said the attack would target killers, not innocent refugees.
The Rwandan government has indicated that it would welcome home the remaining refugees, despite growing insecurity within its borders since the repatriation of more than a million Hutus towards the end of last year. Rwanda's Tutsi- led army is blaming returned Hutu guerrillas for a series of recent attacks on Rwandan civilians and foreign aid workers.
"This time we would screen returnees at the border," says Major Emmanuel Ndahiro in the Rwandan capital, Kigali.
But the 200,000 Rwandan Hutus who remain inside Zaire show no signs of preparing to go home.
The UN says most are being prevented from leaving by militants in their midst.
Meanwhile, the lives of hundreds of children and elderly people in the refugee camps are at risk, and an unknown number are said to have died already.