John Garang, head of the Sudan People's Liberation Army (SPLA) began talks late on Thursday afternoon with Khartoum's First Vice President Ali Osman Mohamed Taha at an exclusive resort in Naivasha, a town 90km northwest of the Kenyan capital Nairobi.
"It's one-on-one," an official at the talks in Naivasha said on Friday, meaning the two were meeting without aides.
The war, which has been raging since 1983, pits the government against rebels seeking more autonomy in the south.
Peace talks have stumbled in recent months after reaching a breakthrough outline accord more than a year ago.
The next round of the formal peace talks is due to start on 10 September.
Garang, who arrived in Nairobi on Thursday afternoon, said the SPLA was committed to the peace process, but declined to say what concessions he was prepared to make at his talks with Taha.
"Obviously it is going to be a critical meeting," Garang told a news conference at Nairobi's Wilson Airport upon his arrival. "The time has come to resolve the Sudan conflict."
"We are under pressure from the Sudanese people. They want peace and we want peace"
John Garang, SPLA chief
"We are going to Naivasha to save the (peace) process from collapsing. It is now time for the process to show some tangible results," he said.
Garang reiterated that the major issues of disagreement were how to carve up power, including the presidency and wealth - especially oil.
He said other issues included security and the tussle over the three conflict areas -- Abyei, Nuba Mountains and Southern Nile, claimed by both sides.
Asked if the United States was putting pressure on Sudanese warring sides to reach an agreement, Garang said the SPLA welcomed contributions from outside parties, adding, "We are under pressure from the Sudanese people. They want peace and we want peace."
Sudan's independent al-Sahafa daily reported that the talks between Garang and Taha had been arranged with the help of the US, Egypt and Kenya.