Police fired teargas to disperse a crowd that was protesting on Sunday against the murder of five people in Riverside near Mathare.
Parts of the city have been gripped by tension since Friday when at least five people were killed in violence involving the police and NASA supporters who were accompanying their leader Raila Odinga after a trip abroad.
Japheth Koome, the police commander in the city, said investigations had started after five bodies were found in the Mathare Area Four slum on Sunday morning.
"We went there and found those bodies with injuries," he told a news conference, describing the murders as a criminal act rather than ethnic-driven violence.
The violence took place a day before the Supreme Court rules on two cases seeking to nullify the re-election of President Uhuru Kenyatta in a repeat election held last month.
Raila, who successfully petitioned against Kenyatta's initial victory in the August 8 vote and subsequently boycotted the repeat poll, visited the scene of the murders on Sunday and accused the government of being behind the killings.
"Those who are doing these acts are the ones who already lost and want to hold onto power by force but we will remove them using the power of the people," he told a crowd of his supporters.
Police fired teargas and used water cannons to disperse protesters for the better part of the morning until calm was restored in the area in the afternoon.
Communications Authority of Kenya said it had banned live broadcasts of political rallies, after all the main TV stations showed hours of live footage of the chaos that greeted Raila's return.
A source at the authority told Reuters on Sunday the ban was put in place to help manage the tension in the country.
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