A reporter for VOA's French to Africa service said police acted after people leaving a mass at Kinshasa cathedral began shouting slogans considered hostile to Kabila. Officers fired tear gas, followed by warning shots.
Two people were wounded, and the crowd began running in all directions.
During the mass Friday, Catholic Church leaders urged Kabila to honor a 2016 church-mediated political deal that called for the president to hold elections and step down.
Kabila has stayed in office more than a year past the end of his second term, the maximum allowed by the DRC's constitution. Security forces fired on anti-Kabila rallies in the capital on New Year's Eve, killing seven protesters.
In an interview Thursday with VOA's French to Africa service, Kabila adviser Julien Lubunga criticized the church for siding against the president.
'It is not up to the church to identify with a certain category of politicians, especially the opposition,' Lubunga said. 'You see, today, in Kinshasa Cathedral, masses are celebrated in the presence of the members of the opposition, whereas the church should gather all the politicians and not to say that there are good people on one side and bad one on the other.'
The church and opposition have voiced concern that Kabila, who has ruled the DRC since 2001, will attempt to remove term limits from the constitution or otherwise maneuver to stay in power.
Lubunga denied this, saying Kabila has stated many times 'that he will comply with the constitution and that after his two terms, he will cede power to an elected president.'
The DRC government recently said the long-delayed polls will take place on December 23. Lubunga said opposition parties 'are afraid to go to the elections' and accused Cardinal Laurent Monsengwo of going against the views of his own church members.
The body of Catholic dioceses in Congo, known as CENCO, said Thursday the government is mounting a campaign of misinformation and defamation against the church.
'Do not be deceived. They just want to manipulate people to believe that the church is divided,' CENCO spokesman Donatien Nshole told VOA on Thursday.