Opposition leader Raila Odinga's party earlier on Friday called for three more days of protests from next Wednesday against tax hikes that Ruto signed into law last month.
Ruto beat Odinga in last August's election. He pledged to be a champion for the poor, but his critics say the tax rises will hurt Kenyans already struggling to afford basic commodities such as maize flour.
"Elections ended August 9 last year. You cannot look for the leadership of this country using the blood of the citizens, the death of the citizens and the destruction of property," Ruto said at the opening of a road in the town of Naivasha.
"These demos will not happen. Listen to me carefully: You cannot use extrajudicial, extra-constitutional means to look for power in Kenya."
Odinga has failed to win the last five presidential votes, but has secured senior positions in government in the past by making deals with those in power following spasms of unrest.
The most recent demonstrations took place despite bans by the police, and Ruto did not say how he planned to stop the upcoming protests.
Kenyan authorities have blamed the deaths on the protesters, some of whom have thrown rocks at police and vandalized public property. More than 300 people were arrested in connection with Wednesday's protests.
The United Nations voiced concerns Friday over the deadly violence surrounding the anti-government protests in Kenya, including allegations of a heavy-handed response by the police.
"The U.N. Human Rights Office is very concerned by the widespread violence, and allegations of unnecessary or disproportionate use of force, including the use of firearms, by police during protests in Kenya," spokesman Jeremy Laurence said in a statement.
Laurence cited reports suggesting that "up to 23 people have been killed and dozens injured" in the demonstrations in the past week, which is higher than the official figure.
"We call for prompt, thorough, independent and transparent investigations into the deaths and injuries. Those responsible must be held to account. Effective measures to prevent further deaths and injuries must be adopted," he said.
"In light of calls for further protests next week, we call on the authorities to ensure the right to peaceful assembly as guaranteed by the Kenyan constitution and international human rights law," Laurence added.
Meanwhile UNICEF, the U.N. children's agency, said it was deeply concerned about the safety and well-being of children in Nairobi and other parts of Kenya during the protests.
"The reports of children being exposed to tear gas and other dangers present in large crowds are alarming," it said, calling for all parties involved to ensure the safety and protection of children.
Information for this report came from Reuters and AFP.