PREMIUM TIMES reported how multiple sources present at the scene said many persons were killed while others were injured.
Despite video evidence, the Nigerian Army denied shooting at protesters. The state governor, Babajide Sanwo-Olu, admitted that there was shooting but claimed nobody died in the attack.
He also said the state government will investigate the incident.
Reacting to the incident, Mr Guterres in a statement signed by his spokesman, Stephane Dujarric, said recent developments in Nigeria are condemnable.
The statement was published on the United Nations website on Wednesday.
The UN Secretary-General also called for an end to reported police brutality and abuses.
"He condemns the violent escalation on 20 October in Lagos which resulted in multiple deaths and caused many injuries. He expresses his condolences to the bereaved families and wishes a speedy recovery to those injured. He calls on the Nigerian authorities to investigate these incidents and hold the perpetrators accountable.
"The Secretary-General urges the security forces to act at all times with maximum restraint while calling on protestors to demonstrate peacefully and to refrain from violence.
"The Secretary-General encourages the authorities to swiftly explore avenues to de-escalate the situation. He reiterates the readiness of the United Nations to support national efforts towards finding a solution."
Earlier, American leaders, Joe Biden and Hillary Clinton had called on President Muhammadu Buhari to halt attacks on citizens.