Violent clashes broke out again on Sunday night.
The extent of the destruction in the town was unclear, but reports from aid workers and south Sudan politicians at the time of the fighting told of bodies lying in the streets.
They said there had been looting and that inhabitants' huts and buildings had been set on fire.
People from both the Dinka and Missirya ethnic groups that lived in Abyei have fled or been evacuated, leaving the town deserted.
Ted Chaiban, the Sudan representative for the UN's Children's Fund (Unicef), said that half of the approximately 30,000 people displaced by the Abyei clashes were children.
Al Jazeera has also learnt that two officials who represent the ruling National Congress in Abyei have disappeared, believed to have been seized by SPLA forces.
But the SPLA has not confirmed that it is holding the men.
Zakaria Atem, one of the National Congress party representatives who has disappeared, is a deputy to Kwal Arrob, the sultan of Abyei.
Zakaria is a senior Dinka Ngok politician whose own household is divided between those loyal to Sudan People's Liberation Movement (SPLM) and those loyal to the National Congress.
The impoverished settlement is in a contested district on the border between north and south Sudan.
While the north currently holds special administrative rights over Abyei, a referendum in 2011 will decide whether it retains its special administrative status in north Sudan or is incorporated into the south.
The clashes began on Wednesday and has exacerbated tensions between north and south Sudan, which fought a 21-year civil war that ended with a peace agreement in 2005.
But the impasse over the Abyei area - whose oil wealth is contested by both north and south Sudan - is one of the stumbling blocks delaying implementation of the peace deal.
Hilde Johnson, the visiting deputy executive director of Unicef, has said the ongoing conflicts in Abyei and Sudan's western Darfur region are derailing plans to put more children in school.
The UN dispatched an emergency assessment team to the region on Saturday.
Antonette Miday, a UN spokeswoman in southern Sudan, said another UN team had been dispatched to Abyei's neighbouring state of Warrap.