The assailants attacked the soldiers as they were sleeping in their tent, the sources told AFP, adding that they then set fire to the tent.
"An army vehicle arrived not far from my house and I saw four bodies of soldiers that they were transporting as well as another soldier with blood all over his body and wounds," one resident said by telephone.
The regional army commander, Brigadier General Marcellin Assoumani Issa Kumba, confirmed the attack but said he could not confirm the death toll.
"We are in full pursuit of these bandits," he told AFP, adding that "the situation is under control for the moment."
A large contingent of soldiers could be seen patrolling the Kananga airport, while the streets of the city of around one million inhabitants were deserted and churches called off Sunday services.
Early this month three suspected militiamen were killed in fighting with soldiers near the airport.
The violence in Kasai erupted after a tribal chieftain known as the Kamwina Nsapu, who rebelled against the regime of President Joseph Kabila, was killed in August 2016.
More than 3,000 people have died in the region and some 1.4 million have been displaced since then.
Two UN experts were killed in March last year while investigating violence in the region, where the United Nations has counted more than 80 mass graves.
Elections were supposed to take place by December 2017, but they were repeatedly postponed -- officially because of the violence in Kasai.
Kabila, 46, has been in power since 2001, at the helm of a regime widely criticised for corruption, repression and incompetence.
The International Federation for Human Rights (FIDH) in December accused the authorities of committing "crimes against humanity perpetrated to create chaos".
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