The Security Council delegation arrived in Juba, the capital of southern Sudan, for a brief visit and to meet with the regional president Salva Kiir.
Following the hour-long closed-door meeting, President Kiir told reporters that the subject of renewed hostilities in Abyei between the Sudanese Army and Sudan People's Liberation Army (SPLA) was discussed.
The fighting, which began on May 13, resulted in widespread destruction in Abyei and the displacement of as many as 50,000 people.
President Kiir confirmed reports this week that the Khartoum government of President Omar al-Bashir is deploying more than 1,000 additional troops to the disputed region.
"I have already called upon him [President Bashir] to intervene to order his military commanders to pull out their forces from Abyei area," he said. "We are not going to fight them."
President Kiir, who is also vice president of Sudan and commander in chief of the SPLA, said if the Sudanese Army troops continue to move to the area in large numbers it would be a violation of the 2005 Comprehensive Peace Agreement, which ended two decades of war between north and south Sudan.
British Ambassador John Sawers, who is leading the Security Council delegation in Sudan, said in response to reporters' questions that the delegation would raise the issue of Abyei during talks in Khartoum with President Bashir.
"The Security Council will be talking to leaders in Khartoum, including President Bashir, on all the issues before the council, the question of the CPA, Darfur and including the recent incidents and the forced displacement of tens of thousands of people from Abyei," he noted.
North-South tensions have been rising for months, with the south accusing the government in Khartoum of delaying implementation of the CPA. The dispute over Abyei and its oil wells is one of the key issues jeopardizing that fragile peace.
The Security Council is to meet with President Bashir on Thursday, during which Abyei, the Comprehensive Peace Agreement and the U.N.'s efforts to deploy 26,000 peacekeepers to Sudan's war-torn Darfur region will top their agenda. Before meeting Sudan's president, the council will make a brief visit to ElFasher in West Darfur.