"Two young people were killed in the parish of Saint-Alphonse de Matete", in the east of the country, while another died in the Masina area, police spokesman Colonel Pierrot-Rombaut Mwanamputu said in a televised statement.
Impatience boiled over on Sunday, with all the country's main opposition and civil society groups joining in the call for peaceful protests.
Kabila has ruled since 2001 and was due to step down in December, but an election to select a new leader has been delayed by his administration to the extent that one is not planned until December 2018.
Internet was restored in the Democratic Republic of Congo on Tuesday after the government cut services for three days on the eve of protests against the president, AFP reporters said.
Protesters want President Joseph Kabila to promise he will not further extend his time in power in DR Congo, a mostly Catholic former Belgian colony.
The poll is now scheduled for December 23, 2018.
A government statement said one policeman had also been killed. "What's more, you have a white man with you - that's a race that causes us problems".
One parishioner who identified herself as Chantal said: "People fell, first-aiders are resuscitating old ladies who have fallen" - but added the priest carried on saying mass.
Speaking to the publication, Telecommunications Minister Emery Okundji said the decision was rooted in "state security" and "the government has the duty to take all measures to protect Congolese lives".
The Secretary-General went on to urge all Congolese political actors to remain fully committed to the 31 December 2016 political agreement, "which remains the only viable path to the holding of elections, the peaceful transfer of power and the consolidation of stability in the DRC".
The police had banned the demonstrations and said that all gatherings of more than five people would be dispersed to ensure public order.
The last demonstrations on any great scale were in July 2016, when veteran opposition leader Etienne Tshisekedi, who died in Brussels the following year, returned home.
Vital Kamerhe, head of the third biggest opposition party in parliament, argued that the presence of priests in Sunday's demonstrations showed that the protest movement had gone into "higher gear".
Florence Marchal, spokesperson for the United Nations peacekeeping mission in Congo, said security forces had shot dead at least seven people in Kinshasa.