He also said injured Sudanese soldiers were unable to receive medical treatment because of the fighting.
Clashes in the area were sporadic, with the AFP news agency reporting one aid worker as saying: "Fighting started this morning at 4am [01:00 GMT]. The SPLA attacked. There's a lull at the moment, but I don't think anybody thinks it's over."
The Sudanese army has issued a statement holding the SPLM responsible for the deteriorating situation in Abyei.
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 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.
Mohamed Vall, Al Jazeera's correspondent in Sudan, said the situation in Abyei was deteriorating.
"After a day of calm yesterday fighting broke out again today - this is the fiercest flare up of violence since the fighting started a week ago ... The situation is still very volatile," he reported.
He said thousands of people had fled the clashes.
"The overall situation is that they [those who fled] are in a very precarious situation - they don't have food and they don't have water."
Tuesday's violence erupted one day after UN agencies and aid workers began distributing food to some of the 30,000 to 50,000 people displaced by fighting last week that levelled the marketplace in Abyei.
The UN warned on Monday that continued insecurity posed challenges to humanitarian relief efforts in the area.
The organisation last week evacuated its entire civilian staff from the town following days of fighting between government forces and the SPLA.
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 have 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.