"We do not think the negotiations have failed and we are ready to continue the negotiations," said spokesman for the Sudan Liberation Movement (SLM), Abd al-Jabbar.
Speaking to Aljazeera, Majthub al-Khalifa, chief negotiator for the Sudanese Government, also called for a continuation of talks, but blamed US officials for undermining the process.
"There have been some differences over some issues but we do not think that we cannot cope with them. We have made very good progress in the humanitarian file. But the real difficulties came after the US and Security Council draft resolutions which would complicate the issue", he said.
But the Justice and Equality Movement (JEM), the other rebel group involved in the talks which began three weeks ago but has not made much progress, on Wednesday said the negotiations with Khartoum had collapsed.
UN estimates put the number of
dead at about 50,000
Muhammed Ahmad Tugod, the chief negotiator for the JEM said: "The negotiations have collapsed already because there are differences, strong differences between us and the Sudanese Government."
The conflict in Darfur has been labelled by US Secretary of State Colin Powell as "genocide", and the US has held the government of Sudan and the Janjawid militia responsible.
Meanwhile, the US has said it will push for a vote by Friday on a UN resolution it brought before the Security Council despite a possible veto from China.
The US draft resolution threatens to impose sanctions on Sudan's oil industry if Khartoum does not rein in the Janjawid, which is blamed for violence in Darfur that has left an estimated 50,000 people dead and almost 1.4 million displaced.