The government had banned the demonstration and cut off all cell phone and internet access to hamper the rally against President Joseph Kabila who is clinging to power. Church groups had called for the rally.
"Since 7am we have received three injured people from the Catholic march. Two were seriously injured and one died from a bullet wound in the chest," said Dr. Francois Kajingulu of the St Joseph de Limete hospital in downtown Kinshasa.
Two more people were reported wounded in the northeastern city of Kisangani.
President Kabila has been in power since 2001, and his mandate expired in December 2016. In negotiations with the political opposition, Kabila was allowed to stay in power beyond his mandate on condition that elections be held by the end of 2017.
The government failed to organize a vote last year and now say an election is being planned for the end of 2018. But election officials have indicated that financial and logistical constraints could imperil that plan as well.
Security forces have killed about a dozen protesters during two previous anti-Kabila demonstrations in recent months. The violent police crackdowns stoked fears that the country could be sliding into another conflict similar to that which led to the loss of some five million lives between 1994 and 2003.
On Saturday Kinshasa's police commissioner, General Sylvano Kasongo, announced a goal of "zero deaths" during the protests, when he held a review of his police force.
"It's our population, our countrymen that we are protecting," he said. "I told the policemen not to fire on the population, which is a civilian population that isn't armed."
Hundreds of ruling party supporters had stormed a Kinshasa cathedral on Saturday.
"We have come to take possession of Our Lady of the Congo Cathedral to take part in Sunday mass ... and defend the homeland," Papy Pungu, youth wing leader of the People's Party for Reconstruction and Democracy (PPRD), told AFP.
On Friday, the European Union, Switzerland and Canada issued a joint statement emphasizing the "importance of respecting fundamental rights including the right to demonstrate."