"This morning, the entire population of Abyei town fled the city, which is now almost empty," Doctors Without Borders said in a statement reported by CNN.
The south's Sudan People's Liberation Army confirmed its enemy had taken over the oil-rich border region.
"Abyei has been under attack by the Sudanese armed forces from air and ground," said spokesman Philip Aguer.
Southern Sudan voted nearly unanimously in January to secede and is to become independent in July, but the fate of Abyei, fought over by rival ethnic groups, has yet to be decided.
U.N. Secretary-General Ban Ki-moon's office said the U.N. compound in Abyei was shelled and demanded an immediate cease-fire. The African Union expressed "very grave concern," and the United States urged Sudanese forces to leave.
Visiting Khartoum Sunday, French U.N. Ambassador Gerard Araud demanded an immediate withdrawal in the name of the Security Council, the BBC reported.
On Saturday, Sudanese President Omar al-Bashir abolished Abyei's joint administration. The north said it moved in after 22 of its soldiers were killed in a southern ambush Thursday.