"The secretary general calls on the government and national security forces to exercise restraint and to uphold the rights of the Congolese people to the freedom of speech and peaceful assembly", Guterres' spokesperson said.
Congo police spokesman Col. Pierrot Mwanamputu, however, said the two were killed after an altercation with police.
Impatience boiled over on Sunday, with all the country's main opposition and civil society groups joining in the call for peaceful protests.
Congo's election commission has set a new date for presidential and legislative elections, which is to be held on December 23, 2018, though the opposition has said it would only agree to delay the vote until June 2018.
The government refused permits for the demonstrations Sunday, and shut down internet and SMS services countrywide ahead of the planned anti-government protests for what it called security reasons.
The protesters were demanding that Kabila promise he will not seek to further extend his time in power in Democratic Republic of Congo, a mostly Catholic former Belgian colony.
The poll has since been postponed until December 2018.
A government statement said one policeman had also been killed.
The Roman Catholic archbishop of Kinshasa, Laurent Monsengwo Pasinya, issued an angry statement, saying that the marches had been "peaceful and non violent". "What's more, you have a white man with you - that's a race that causes us problems".
The episcopate, gathering the country's bishops, said "vile acts" had been committed. She also said that dozens, including some priests, have been detained.
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".
United Nations chief Antonio Guterres has urged Kabila who has been in power since 2001, to abide by an agreement to step down ahead of elections slated for later this year.
"The major deployment of police, army and military gear aims at discouraging people who are tempted to go out and demonstrate", said Congolese analyst Jacques Wondo.
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".
"With each step we have to amend our mistakes".
"If you don't clear out of here, I'll order that you be shot at", he said.
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