The peace talks, which began in the Qatari capital Doha on Tuesday, are the first to be attended by both the Sudanese government and the rebel fighters since 2007.
On Wednesday, Khalil Ibrahim, the JEM leader, and Nafie Ali Nafie, presidential aide and head of the government delegation, held face-to-face talks which both sides described as "positive".
'Disband Arab militias'
Mediators have been at pains to stress the Doha talks are preliminary negotiations aimed at paving the way for a broader peace conference on Darfur at a later date.
At the outset of negotiations, Ibrahim said wider peace negotiations following the Doha talks would only be possible if Khartoum disbanded allied Arab militias in Darfur and allowed rebel representation in the central government.
He also called for confidence-building measures including the release of prisoners and expansion of aid provision to rebel-held regions.
By turn, Nafie reiterated "Sudan's determination to continue down the path of peace".
The United Nations has estimated that 300,000 people have died and more than 2.2 million fled their homes since rebel fighters in western Sudan rose up against Khartoum in early 2003.
The Sudanese government puts the death toll at 10,000.
Also on Saturday, Ahmed Abul Gheit, the Egyptian foreign minister, held talks with Omar al-Bashir, the Sudanese president, amid reports that the International Criminal Court (ICC) has decided to issue a warrant for al-Bashir's arrest.
However, a spokesman of the ICC insisted that "at this moment, there is no arrest warrant".
Mahjub Fadl, al-Bashir's spokesman, also denounced any move to launch proceedings against the Sudanese leader in connection with the Darfur conflict.