Nyamira Senator Okong'o Omogeni has called on security agencies to practice restraint while dealing with unarmed protesters.
He spoke on Wednesday during Senate proceedings.
"As we move forward we also demand accountability from our security forces," Omogeni said.
The senator noted that there are groups in history which have held peaceful protests that brought change.
Omogeni said if a protester breaks the law, then they ought to be presented before the court, and not to be shot.
He alleged that up to eight Kenyans lost their lives when protesters breached parliament in last week's protests.
The police were in June this year banned from using excessive force on peaceful protesters.
The High Court ruling in Malindi issued temporary orders preventing security agencies from using lethal and other less-lethal ammunition against peaceful protesters.
This included the use of water cannons, tear gas, and rubber bullets during protests.
High Court Judge Justice Thande emphasised that violence against peaceful protesters is prohibited.
However, police went on to defy the court order on Wednesday and used excessive force on the peaceful protesters.
As of July 1, the Kenya National Commission on Human Rights reported that at least 39 people had died.
KNCHR said 361 persons were injured from the nationwide protests.
The commission also reported 32 cases of enforced disappearances and 627 instances of arrests of protestors.
The Commission said the data was recorded from June 18 to July 1, 2024.
KNCHR said the deceased victims were from Nairobi (17), Nakuru (3) Laikipia (1), Narok (1), Kajiado (3), Uasin Gishu (4) Kakamega (1) Kisumu (2), Kisii (1), Mombasa (3), Siaya (1), Kiambu (1) and Nandi (1).