The Sudanese government and the southern rebel Sudan People's Liberation Army (SPLA) have been fighting since 1983 over religious freedom, oil, and the right for the south to rule itself. Some two million people have died in the conflict.
Sumbeiywo said he had been asked by regional leaders to seek a breakthrough.
"I think they don't have an option," Sumbeiywo told Reuters by telephone from Nanyuki, central Kenya, where the delegates met.
"Heads of state in the region are putting pressure (on both sides), and they have given me the go-ahead to pressurise the parties to agree."
Sumbeiywo, who heads the team mediating the talks under the regional Inter-governmental Authority on Development (IGAD), said he expects the talks to break new ground though a comprehensive peace deal is unlikely.
The discussions are scheduled to continue until 24 August. IGAD mediators have previously said they were aiming for a peace accord this time round.
Talks broke down last month after the government rejected a draft accord prepared by IGAD. The two sides failed to agree on how to carve up power and wealth, including oil.
They are also at odds on how to structure the army, where to put the capital and how to settle the issue of three areas, Abyei, Nuba Mountains and Southern Blue Nile, all of which are claimed by both sides.
IGAD comprises the east African states of Djibouti, Eritrea, Ethiopia, Kenya, Sudan, Uganda and, nominally, Somalia.
The Sudanese government in July attacked mediators’ proposals that the army and central bank be split between north and south.
“Never before have the two parties been so close to reaching a comprehensive peace agreement,” Amara Essey, interim chairman of the African Union said in a statement issued from his base in Ethiopia, Reuters reported.
“The people of Sudan expect and deserve peace to end the trauma caused by the conflict,” he added.
In the Kenyan town of Machakos last year, Khartoum and the SPLA struck a breakthrough deal with the south being granted the right to self-determination after a six-year transition period. The largely Christian/Animist region was also exempted from Islamic law.
Sudan has been in a state of civil war almost constantly since it achieved independence in 1956.
As a prelude to the most recent bout of talks, the government released a number of political detainees.
It also said the Islamist leader Hassan al-Turabi, jailed in 2001 on charges of undermining the government's authority, will be freed, our correspondent said.