They made the pledge during a reception in Khartoum that Vice President Ali Osman Taha of the ruling National Congress party held in honor of an SPLM delegation visiting Khartoum to discuss how to implement the deal.
"We are determined to protect and implement the peace agreement, strengthen our partnership with the National Congress and work together to find a solution to the Darfur problem on the basis of what has been agreed upon in the peace agreement," said SPLM Secretary General James Wani.
The agreement Khartoum signed with the SPLM addressed many of the grievances of the south and contained specific mechanisms for power- and wealth-sharing as well as granting greater autonomy to southerners.
Khartoum and the SPLM hope the model can be used to bring peace to Darfur, where some 300,000 people have died and nearly 2.4 million displaced in more than two years of conflict with ethnic minority rebels.
"The Darfur problem can be solved through peaceful negotiations if there is the determination that has contributed to reaching the peace agreement for the south," said Wani.
Taha agreed and reiterated his government's "resolve and seriousness in finding political solutions to all problems of the Sudan, including those of Darfur and the east".
Like their counterparts in Darfur, ethnic minority rebels in the eastern states of Red Sea and Kassala complain of marginalisation by the Arab-dominated regime in Khartoum.
Taha said the peace agreement with the south "has become a basic document acceptable to all sectors of the Sudanese people and approved by all of the country's political institutions".
He added: "We are resolved to reach a peaceful settlement to the Darfur problem through negotiations."
Khartoum and Darfur's two main rebel groups, the Sudan Liberation Movement and the Justice and Equality Movement have held at least two rounds of unsuccessful talks under the auspices of the African Union.