The two sides had met for talks several times in the last few days to try and reach an agreement to end the fighting, but each agreement has been broken by further clashes.
But Edward Nino, political supervisor of the SPLM, denied the group had given up its commitment to the peace deal.
"It has been reported that the SPLM was not committed to the comprehensive peace agreement," Nino told Al Jazeera.
"However, I say that if it was not for the SPLM stance, we would have returned to war a long time ago."
The status of the area remains contested between north and south Sudan three years after the end of the country's civil war.Civilians flee
Usama Sayyid Ahmed, Al Jazeera's correspondent in Abyei, said a large number of civilians, including women carrying children, were fleeing the fighting.
He also said injured Sudanese soldiers were unable to receive medical treatment because of the fighting.
Clashes in the area were sporadic on Tuesday, with the AFP news agency reporting one aid worker as saying: "Fighting started this morning at 4am [0100 GMT]. The SPLA attacked. There's a lull at the moment, but I don't think anybody thinks it's over."
The fighting in Abyei has killed an undetermined number of people. A majority of the town's civilians - between 30,000 and 50,000 -have been displaced, according to the UN.
Tuesday's fighting, which had broken an earlier ceasefire, was set off by an assault on the town by the southern Sudan People's Liberation Army (SPLA) with tanks and infantry, firing rockets and mortars.
The UN has pulled out most of its 250 civilian staff of the town, leaving just the 400 peacekeepers on the ground.
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.