The U.N. Mission in Sudan, or UNMIS, warned Khartoum it was responsible for law and order amid reports thousands of civilians were fleeing southwards after northern Sudan Armed Forces troops and tanks overran the border town Saturday.
"UNMIS strongly condemns the burning and looting currently being perpetrated by armed elements in Abyei town," read its statement.
The mission also called on the "government of Sudan to urgently ensure that the Sudan Armed Forces fulfill their responsibility and intervene to stop these criminal acts."
Abyei's seizure, in the run-up to international recognition of southern independence in July, has been condemned by the world powers as a threat to peace between north and south Sudan.
Soon-to-be independent south Sudan also claims Abyei district, which has a special status under a 2005 peace deal that ended 22 years of civil war, and has called the occupation "illegal".
"The SAF are still occupying Abyei and they continue to bomb," Deng Arop, the region's administrator who fled the violence and took shelter in Waw, a town almost 200 kilometers south of the disputed area, told Agence France Presse.
He said that bombings of east and south Abyei proved the northern army intends to "advance further south" and that the continued "indiscriminate bombing" would only aggravate the "humanitarian crisis."
The United States urged Sudan to withdraw its forces from Abyei district.
Princeton Lyman, the U.S. envoy for Sudan, said the "occupation" of Abyei by northern troops is "an extremely disproportionate response by the government of Sudan" to an attack on a U.N. convoy escorting the troops last week.
A U.N. Security Council delegation headed Monday to Juba for talks with southern President Salva Kiir, after saying they were "very, very concerned about the rapidly deteriorating situation in Abyei."
"The members of the Security Council call upon the government of Sudan to halt its military operation and to withdraw immediately from Abyei town and its environs," French ambassador to the United Nations Gerard Araud said earlier.
Senior U.S. Senator John Kerry warned of the dangers of a return to conflict and told Khartoum it risked torpedoing a promised rapprochement with Washington.
"At this very moment, Sudan stands ominously close to the precipice of war," said Kerry, who chairs the influential Foreign Relations Committee.
Angry Sudanese rallied in the southern capital, meanwhile, demanding northern forces end their "invasion" of Abyei.
"The north must leave, this cannot be allowed," said demonstrator Choul Deng, who comes originally from the region on the north-south border.
"The north are acting like they did during the days of the civil war, bombing and attacking our people."
Waving banners and shouting slogans, more than 100 demonstrators marched through the streets of Juba, starting at the grave of the late rebel leader John Garang, who led the south during the civil war with the north.
"People are suffering," said Charles Deng, a student. "Their homes are being destroyed by the tanks of the north."
Abyei was granted a special status under the 2005 Comprehensive Peace Agreement, which requires both sides to keep their troops out until a vote on its future.
The fighting has soured the mood in the southern capital Juba.
"We fear that this can lead to something bigger, back to war," said businesswoman Mary Okech.
Southern officials have vowed it will not impact the south's independence, due in less than two months.
However, activists have warned of the severity of the situation.
"We always talk about proverbial forks in the road," John Prendergast, co-founder of the U.S.-based Enough Project campaign group, told AFP. "This is a real one between war and peace between the north and south."
Prendergast, whose satellite project -- backed by Hollywood star George Clooney -- monitored a troop build-up in the Abyei area in the weeks before the fighting, warned any deal to resolve the conflict must put pressure on leaders rather than offer incentives.
The European Union meanwhile allocated on Monday 200 million euros ($280 million) in aid to help south Sudan combat poverty when it becomes an independent state.
Abyei was due to vote on its future in January alongside a referendum on independence for the south, which delivered a landslide for secession.
But the plebiscite was postponed indefinitely as the north and south disagreed on who should be eligible to vote in an area where conflicted loyalties and land disputes keep tensions high.(AFP)