He said the decision to deploy peacekeepers for a limited period had been taken in response to an appeal from Kazakh President Kassym-Jomart Tokayev and "in view of the threat to the national security and sovereignty of the Republic of Kazakhstan caused, inter alia, by outside interference".
Tokayev had earlier asked for help from the Collective Security Treaty Organization, a military alliance of Russia, Belarus, Armenia, Kazakhstan, Kyrgyzstan and Tajikistan.
Pashinyan did not say how many peacekeepers would be sent, or when they would arrive.
Unrest continues in Kazakhstan as some demonstrators at mass protests over soaring fuel prices turned violent.
Around Kazakhstan - five times the size of France with a population of nearly 19 million - protests killed eight police and national guard troops on Tuesday and Wednesday, Russia's state-owned Sputnik agency quoted the Kazakh interior ministry as saying.
Interfax news agency quoted Leonid Kalashnikov, head of a Russian parliamentary committee that deals with relations with the Commonwealth of Independent States, as saying the peacekeepers would stay "until the situation stabilises".