The Orange Democratic Movement (ODM) party is now calling for the unconditional release of protesters on Thursday.
In a statement on Friday, the party said it is aware at least 70 persons were arrested in the demonstrations.
It said some of those arrested were persons with disability.
The party called on relevant authorities to ensure their immediate release.
"The ODM party is asking for the unconditional release of the over seventy Kenyans who were arrested yesterday during the public protests in Nairobi and other parts of the country.
"The majority of them are being held at the Central Police Station in Nairobi. It is worth noting that some of these arrested are persons living with disability (PWDs)," ODM said.
The party insisted that the Constitution of Kenya allows for Freedom of Expression, Public picketing and protesting to present petitions to the government and make their case heard.
On Thursday, a section of Kenyans took to the streets to protest in a day that was dubbed "Nane Nane".
During the demos, several people were arrested by the police even as they engaged in running battles.
There was heavy deployment of anti-riot police officers ahead of the demos.
Some are stationed in strategic locations, others are patrolling on foot while others are using trucks.
Nairobi remains the heart of protests as other parts of the country that previously experienced protests remained relatively calm.
