The Roman Catholic Church is powerful in the country, but the protests were also supported by many evangelical and other churches, and Muslim leaders.
A spokesman for the national police told state television that "two people were killed" in the capital, while nine policemen were wounded, two of them seriously. Their clothes have been torn, " Georges Kapiamba, the president of the Congolese Association for Access to Justice told reporters.
Several people were also killed in New Year's Eve protests organised by the church.
"The Secretary-General, once again, calls on Congolese political actors to work towards the full implementation of the 31 December 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 [country]", the statement concluded.
Mr. Guterres called on the Congolese authorities to conduct credible investigations into these incidents and to hold those responsible accountable. The Church also called for the demonstrations in late December which led to at least seven deaths, according to United Nations peacekeepers.
MONUSCO said 94 people were arrested across the country.
"If they decide to repress, there will be no peace". The so-called "secular committee of coordination" has called on people to march after mass "with our peace branches, our Bibles, our rosaries, our crucifixes, to save the Congo". "I'm terrified for my children, who have been alone since December 28", said Kandolo, a member of the group in Kinshasa.
"We're scared. I'm just like everyone else, I'm scared".
People have grown increasingly angry with Kabila since he refused to step down when his term expired in December 2016.
Under the deal brokered by the Catholic Church, Kabila was to organise elections in 2017.
Critics accuse Kabila of postponing elections to maintain his grip on power, while worldwide observers have warned that Congo's political tensions could further destabilize the impoverished country and the region at large.
The authorities later blamed organisational problems for a new delay until December 23, 2018 - a postponement that has angered Western nations, but one that they have reluctantly accepted.