U.N. officials heard sporadic gunfire outside Abyei town later in the morning, but later found no signs of an attack, said U.N. spokeswoman Hua Jiang. A diplomatic source said they had earlier witnessed the burial of 33 bodies of people caught up in the violence.
The U.N. Security Council discussed the issue on Thursday. After the closed-door meeting, China's U.N. Ambassador Li Baodong, council president for March, said the 15-nation body expressed "deep concern" at the fighting in Abyei.
Analysts say Abyei is one of the most likely places for fighting to break out in Sudan as it prepares for the secession of its south, due to take place in July.
Southerners overwhelmingly voted in a referendum in January to declare independence, under a 2005 peace deal that ended decades of civil war with the north.
Both sides remained at loggerheads over who owned Abyei, a fertile, oil-producing border area used both by northern Arab Misseriya nomads and the south-linked Dinka Ngok people.
Washington, the United Nations and other world powers that helped broker the accord have urged Sudan's leaders to settle the Abyei crisis and avoid a return to civil war.
Li said the Security Council saw an "urgent need for a political agreement" on Abyei.
The north-south conflict killed an estimated 4 million people and destabilised the region. The northern and southern armies have clashed in Abyei since the accord.
Dinka officials in Abyei said Misseriya fighters, backed by Khartoum-supported militias, attacked a police station in the village of Todach on Sunday and Monday, then moved on to the village of Maker on Wednesday.
Misseriya officials accused south Sudan's SPLA army of starting the fighting by attacking a nomadic camp. Khartoum and the northern and southern armies have denied any involvement.
"In the early hours of the morning (on Thursday) 300 women and children left, moving further south," the U.N. spokeswoman said.
A diplomatic source told Reuters: "On Wednesday we witnessed the burial of 33 bodies. We think they were the victims of the past clashes."
The source said some of the bodies wore police uniforms and all were southerners. The burial happened close to Abyei town, south of the scene of the reported fighting.
Tensions have been exacerbated by the onset of the migration season, when the Misseriya drive their livestock through Abyei, into the south searching for pasture.
An earlier deal over guaranteeing the route stalled when Dinka chiefs declined to talk to a Misseriya delegation, saying it was too junior, other diplomatic sources said.
Estimates of the death count have varied widely. Abyei's joint Dinka-Misseriya administration said at least 10 people died Sunday and six Wednesday.
SPLA spokesman Philip Aguer estimated more than 70 may have died since the start of the week.