"It is time for new sanctions to hit [Putin] hard as an individual, [as well as the Russian] energy...[and] banking sector," he said
The U.S. senators are visiting Georgia following a trip to Ukraine and a three-day tour of the Baltic states.
Speaking on December 31 on the front line in Ukraine's eastern conflict zone, McCain promised continued support for Kyiv in the face of aggression from Moscow.
"I send the message from the American people -- we are with you, your fight is our fight, and we will win together," McCain was quoted as saying by Ukrainian President Poroshenko's press service.
"In 2017, we will defeat the invaders and send them back where they came from. To Vladimir Putin -- you will never defeat the Ukrainian people and deprive them of their independence and freedom," McCain said after a visit to a military base in the southeastern town of Shyrokyne.