In an interview with The Associated Press, Moise Katumbi said he was roughed up by police in May who injected him with an unknown substance outside a courthouse in the city of Lubumbashi.
"Their plan was to kill me," Katumbi said yesterday, "because they are scared about my popularity."
Katumbi said the directions came from the highest levels of Congo's government, but he did not provide details about whom he specifically believes was responsible.
Kabila is supposed to leave office in December, but he has not publicly declared his intentions.
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Congo's communications minister, Lambert Mende, was unavailable to comment, but he had previously dismissed allegations Katumbi had been harmed by the police.
He noted that Katumbi was allowed to leave Congo for medical treatment elsewhere.
"If the objective was to kill him as he claims, why let him go and vilify us in the press?" Mende said in a recent interview with a radio station.
Kabila has been in office since 2001, taking over less than two weeks after his father, President Laurent Kabila, was shot by a bodyguard in the presidential palace.
He was elected president in 2006 and again in 2011.
Kabila is barred by Congo's constitution from a third term.
Congo, which has vast mineral deposits, is nearly one-fourth the size of the United States and has a population of more than 79 million.
More than a decade after Congo's back-to-back civil wars ended, the country's east remains in discord.