Security agents fired live bullets into crowds, killing six people.
The UN's Secretary-General Antonio Guterres on Monday called for "credible investigations" after at least six people were killed in the Democratic Republic of Congo during a crackdown on a protest against President Joseph Kabila.
Guterres said the government should "hold those responsible accountable" in a statement issued by his spokesman in New York after live rounds and tear gas were fired to disperse demonstrators in Kinshasa.
The country's powerful Catholic Church, one of the few institutions to enjoy broad credibility nationally, had called for the rallies despite a government ban on all demonstrations.
Guterres "urges the Congolese security forces to exercise restraint", his spokesman said in the statement, and "called upon all concerned to ensure full respect for places of worship".
The UN peacekeeping mission Monusco said six people were killed in Kinshasa and scores injured nationwide in the rallies.
Congolese authorities said two of the deaths were caused by "stray bullets".
Kabila, 46, has been in power since 2001, at the helm of a regime widely criticised for corruption, repression and incompetence.
His constitutional term in office expired in December 2016 but he has stayed on, stoking a bloody spiral of violence.
Under an agreement brokered by the Catholic Church, he was allowed to stay in office provided new elections were held in 2017.
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.