Human Rights Watch Central Africa director Ida Sawyer said Congolese security forces shot dead two men outside St. Alphonse church in the Matete district.
U.N. Congo mission spokeswoman Florence Marchal said at least 82 people have been arrested across the country in connection with Sunday's protests.
Congo police spokesman Col. Pierrot Mwanamputu, however, said the two were killed after an altercation with police.
Georges Kapiamba, a human rights activist, said he had confirmed with his network of observers that security forces killed at least two people in Kinshasa and one in Kananga.
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Kabila, who has been in power since the 2001 assassination of his father, Laurent Kabila, has not ruled out another presidential run through constitutional changes. He said a police officer also died. At least two deaths and multiple arrests were reported.
Opposition leader Vital Kamerhe told Reuters that security forces fired tear gas into the Paroisse Saint Michel during the mass he was attending.
AFP counted about 10 people hurt including a priest with an injury to the face and a woman in her sixties with a gash on her forehead, after police broke up gathering at churches in central Kinshasa.
Checkpoints were set up across country's capital Kinshasa and police were stopping and searching cars and checking passenger's identities.
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Democratic Republic of Congo's government on Saturday ordered telecommunications providers to cut internet and SMS services across the country ahead of planned anti-government demonstrations.
The Catholic church had led calls for peaceful protests on Sunday, with all the vast central African country's main opposition and civil society groups expressing support.
Some 40 per cent of Congo's population is Roman Catholic and the Church enjoys rare credibility with the public, even though its leadership has not formally backed the protests.
Elections were to be held by the end of 2017 under a church-mediated deal between the opposition and Kabila that was agreed a year ago.
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