The appeal made on Saturday coincided with peace talks currently under way in the Nigerian capital of Abuja between the Sudanese government and two rebel groups from Darfur.
"The Security Council is called upon not to take any action to impede the quest of the two parties for securing a solution to the problem," said Sudan's Minister of State for Foreign Affairs Najib Abd al-Wahab.
"The Security Council should assist the two parties to find a way out and also to assist the African Union to properly supervise and monitor the efforts of the parties to secure lasting and cherished peace and security," he added.
The minister said the talks in Abuja were more relevant to the situation in Darfur than that in the Security Council.
"The Security Council is called upon not to take any action to impede the quest of the two parties for securing a solution to the problem"
Sudan’s Minister of State for Foreign Affairs
He said since the two warring parties have seen the need for peace in Sudan, they should be encouraged to achieve it.
According to UN estimates, up to 50,000 people have died in the conflict sweeping Darfur since rebels rose up against the government in February last year.
The conflict has also rendered some 1.4 million people homeless.
The Security Council has ordered that Khartoum disarm the Janjawid, a government-backed militia accused of large scale abuses in the region.
The Council gave Khartoum a 30-day deadline, which expired on Sunday.
Some UN member states want to impose diplomatic or economic sanctions against Sudan. The European Union has threatened to slap sanctions if Sudan fails to rein in the Janjawid.
Rebels must disarm
Foreign Minister Mustafa Uthman Ismail strongly criticised what he called the double standards of the international community in demanding the immediate disarmament of the Janjawid but not putting the same pressure on the rebels, according to the Khartoum press on Saturday.
"The two rebel movements were moving around with their weapons among civilians," the Al-Akhbar Al-Youm daily quoted the minister as saying.
Ismail said that both the African Union's resolution on the Darfur crisis and the abortive ceasefire agreement reached in Chad in April required cantonment of the rebels - getting them to return to their base so they no longer roam the villages - concurrently with disarming the Janjawid.
"But the rebels did not adhere to this condition," the minister said.