Ahmad Hussain Adam, a Jem spokesman, said the government's announcement came as no surprise.
"This has been their intention since the beginning of this conflict, they don't want peace, they want to impose a military solution," he told Al Jazeera.
Delayed peace process
Jem, one of two main Darfur anti-government groups, signed a framework accord in February in Qatar that was hailed by the international community as a major step toward bringing peace to the region devastated by a seven-year war.
However, there was no final, comprehensive peace agreement by a March 15 deadline and Jem broke off from the talks that same month, claiming ceasefire violations.
Shortly afterwards, the government in Khartoum, the capital of Sudan, signed a framework peace deal in Qatar with the Liberation and Justice Movement, another anti-government group that is made up of an alliance of splinter factions.
But Adam, Jem's spokesman, dismissed criticism that his party is partly responsible for delaying the peace process.
"We are not responsible. Our organisation is the one that started the negotiations in Doha and we have been very patient. We know the regime is just using the Doha process as a public relations exercise.
"We asked for the postponement of negotiations, because we would like to reform the process. We don't want the process to be like a public relations process that is used and exploited by the government.
"What we need is a meaningful and serious process."
Talks ruled out
However, Atabani, the chief negotiator of the talks, ruled out further peace talks with Jem.
But he said another round of negotiations with the Liberation and Justice Movement would take place in the first week of June.
Earlier in May, Sudan sought the help of Interpol, the international policing organisation, in a bid to have Khalil Ibrahim, the Jem leader, arrested in Egypt.
A Sudanese special court accused Ibrahim of masterminding an unprecedented attack by Jem on Omdurman, the twin city of the capital.
Darfur has been the site of a devastating civil war since 2003 that has killed 300,000 people and displaced another 2.7 million, according to UN figures.
Khartoum says 10,000 people have died.