Ruto, who is on a diplomatic visit to Germany, said impunity would not be tolerated and all Kenyans must submit to the rule of law.
"That is what makes us equal. Nobody should trample on the rights of others," Ruto said in a statement, adding he would ensure the right to life, property and business was protected.
"We have deliberately offered the police operational and financial independence to work. It is their duty to ensure that everyone adheres to the rule of law," he said.
Veteran opposition leader Raila Odinga has called for regular protests every Monday and Thursday, accusing Ruto of stealing last year's election and of failing to control the surging cost of living.
African Union Commission head Moussa Faki Mahamat on Tuesday voiced "deep concern" after anti-government protests in Kenya turned violent, and appealed for calm.
"The chairperson urges all stakeholders to exercise calm and engage in dialogue to address any differences that may exist in the supreme interest of national unity and reconciliation," Faki's office said in a statement.
Faki "expresses deep concern at violence... which has resulted in loss of life, damage of property and the interruption of certain economic activities," his office added.
The AUC chairperson reiterated solidarity and support of Kenya's government and its people in efforts towards national unity, peace and stability.
On Monday, police fired tear gas in Nairobi and the western city of Kisumu - an Odinga stronghold - to disperse crowds, aiming canisters at cars carrying journalists in the capital, while looters went on the rampage.
Officers also used tear gas and water cannon as Odinga's convoy moved through a congested neighborhood in Nairobi, sending people running for cover.
One man was shot dead in Kisumu, the head of the city's main hospital told AFP, the second fatality reported since the demonstrations kicked off the previous Monday, when a university student was killed by police fire.
Many Kenyans are struggling to put food on the table, battling high prices for basic goods as well as a plunging local currency and record drought that has left millions hungry.
