The deaths are the result of clashes between the army and a rebel group, but civilians have also been caught up in the violence.
The figure, reported by Reuters, is from Catholic Church sources in the country and according to the Church, 20 villages have been completely destroyed, half of them by government troops.
The UN has reported on the discovery of more than 20 mass graves but has put the death toll so far at about 400.
The UN human rights chief, Prince Zeid Ra'ad al-Hussein, said investigators in Kasai province had identified dozens of mass graves along with harrowing evidence of people being shot, burned or hacked to death.
Atrocities were being carried out by the security forces and a government-backed militia, known as the Bana Mura, which was set up to help fight a rival group known as the Kamuina Nsapu, Prince Zeid said.
He added that local authorities had denied the UN access to information about what was happening in the region. The UN has said it has evidence that hundreds of villagers from the Luba and Lulua ethnic groups have been killed.
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The UN Human Rights Council is likely to vote this week on whether to mandate an independent investigation into the violence following what the group's commissioner described as horrific atrocities committed in Kasai province.
The Congolese authorities have said they would reject it.
More than a million people have been displaced in the region in the last year and aid workers say the humanitarian response on the ground has so far been inadequate.
Violence erupted in the once peaceful Kasai region last August, after the death of a local leader during fighting with security forces.
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