The referendum over whether to remain as five states or form a single region runs until Wednesday.
It is being held amid ongoing insecurity and many displaced people have not been registered to vote.
The US has said the vote will not be credible but President Omar al-Bashir insists it will be free and fair.
Bashir defiant on Darfur tour
"If held under current rules and conditions, a referendum on the status of Darfur cannot be considered a credible expression of the will of the people of Darfur," said US State Department spokesman Mark Toner.
The referendum is the last step in a peace process negotiated in Doha. Rebels have long requested more regional powers to end what they see as Khartoum's interference in land ownership conflicts.
If Darfur chose to form one region, it would carry more weight within Sudan, they believe.
But the BBC's West Africa Correspondent Thomas Fessy, who recently visited Darfur with Mr Bashir, says many of those who initially wanted this referendum will be likely to boycott the vote because they say it will not be fair.
More than 2.5m people remain displaced in Darfur and 130,000 more have fled renewed violence this year, the UN says.
Some 300,000 people have been killed since conflict broke out in the troubled region in 2003.
Janjaweed militiamen riding horses spread terror in a multi-layered conflict after rebels took arms against the central government, feeling marginalised.
The Janjaweed were used by the government alongside bombing campaigns. Today, many have been integrated into the Rapid Support Forces, currently fighting in the Jebel Marra region.
The International Criminal Court (ICC) has indicted President Bashir on counts of genocide and war crimes committed in Darfur.
Mr Bashir - who has told the BBC he will step down as president in 2020 - has dismissed the ICC as a "political tribunal".
The western Sudanese region of Darfur is to vote on its administrative status, 13 years after the start of a conflict which has left 300,000 dead.