The region has seen a major spike in violence since September when government forces killed tribal chief and militia leader Kamwina Nsapu who had rebelled against President Joseph Kabila.
The unrest has claimed more than 400 lives and forced some 1.3 million from their homes, according to UN figures.
Unconfirmed local statistics put the number of dead as high as 3,000.
"As far as the violence recorded in the Grand Kasai provinces go, including the murder of two UN experts and the police officers beheaded by the Kamwina Nsapu (militia), the Congolese judicial system will retain charge of the investigations," Human Rights Minister Marie-Ange Mushobekwa told AFP.
"One does not give ultimatums to a sovereign state," she said.
UN rights chief Zeid Ra'ad Al Hussein said on Tuesday he was giving Kinshasa two days to show it was seriously investigating the Kasai violence or submit to an international investigation.
In March, the UN High Commissioner for Human Rights demanded a high-level investigation into abuses committed against civilians in Kasai.
And Washington called this week for a UN-led probe into the murder of two UN experts who had been gathering evidence about 40 mass graves in the region.
Mushobekwa said Congolese officials were working with the UN mission in Congo MONUSCO and the UN office for human rights to probe the violence.
She said the Congolese would seek the help of UN forensic experts "as and when the need arises."
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