South Sudan's Ngok Dinka tribe is holding a unilateral referendum to decide whether oil-rich Abyei, a district they inhabit and is under dispute between the Khartoum government and South Sudan, joins either of the two nations.
Reports said on Sunday that the referendum results were expected on October 31.
The exercise was proceeding peacefully, said Luka Biong, spokesman for the Abyei Referendum High Committee, a civic group that is organising the vote.
The quarrel over Abyei is one of the main unresolved disputes after the 2005 peace agreement between Sudan and South Sudan, which ended a civil war and led to the independence of South Sudan.
Abyei was meant to vote on whether to be part of Sudan or South Sudan in January 2011 - the same day Juba voted overwhelmingly to split from the north - as part of the peace accord.
Both the Sudan and South Sudan governments, along with the African Union, which is playing a mediation role over the district, do not recognise the referendum.
The Misseriya Arab tribes, who come to Abyei to graze their cattle and have closer ties with the government in the north, strongly oppose the unilateral referendum.
About 100,000 Dinkas residing in South Sudan had returned to Abyei for the referendum, which would be conducted over a three-day period.
The Sudanese government says the referendum is illegal and goes against agreements signed between Khartoum and Juba.
Meanwhile, the African Union on Sunday accused the Sudan government of preventing an AU delegation from visiting Abyei following talks that failed to make progress on the flashpoint region.
The AU "expresses its deep disappointment and regret that it was unable to undertake the visit (Saturday and Sunday)", it said, accusing Khartoum of postponing it "for contrived security reasons".
The AU's Council for Peace and Security lamented the "obstruction" to its mission and "reiterates its deep concern at the prevailing situation in Abyei," it said in a statement posted on the internet.
The AU "stresses the need for active and continued African involvement" in resolving the dispute, it said.
A Sudanese foreign ministry spokesman contacted in Khartoum declined to comment on the statement.
The AU, which is mediating in the dispute, was initially headed to Abyei on Tuesday and Wednesday but put off the trip pending the outcome of talks between the Sudanese and South Sudanese presidents, Omar al-Bashir and Salva Kiir.
The talks on Tuesday failed to make any progress on Abyei, though the two leaders also discussed issues such as opening up border posts to residents and traders, the transportation of South Sudan's oil through Sudanese pipelines, as well as security and trade and economic ties.