He warned that Russian Federation continues to "seek to redraw global borders by force, undermine democracies of sovereign nations and divide the free nations of Europe, one against another".
Pence was scheduled to meet with the presidents of the Baltics - Estonia, Latvia, and Lithuania - on Monday.
Meanwhile, Russia codified its diplomatic response to new sanctions passed by Congress last week, as well as their delayed response to Barack Obama's expulsion of 35 diplomats in December.
Trump's presidency brought with it the possibility of improved relations with Russian Federation after the president spent much of the 2016 campaign speaking warmly of Putin and expressing optimism that he would be able to build a strong relationship with the Kremlin.
"We talked about the upcoming [Russian military] manoeuvres near the Estonian border. and how Estonia, the United States and North Atlantic Treaty Organisation should monitor them and exchange information", Ratas said.
Pence is also due to visit Montenegro, the alliance's newest member, and make a stop in Georgia, an aspiring member, which fought a brief war with Russian Federation in 2008.
Pence departed Estonia later on Monday and arrived in Georgia, where he was greeted at the airport by Prime Minister Giorgi Kvrikashvili.
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He went on to say that Russia's recent expulsion of hundreds of USA diplomats won't deter Washington's commitment to security.
Pence's visit is meant to reassure the European periphery of Washington's continued support as Pence's boss Donald Trump continues to improvise his foreign policy on the fly, observers suggest.
Troops from the United States, Britain, Germany, Turkey, Ukraine, Slovenia, and Armenia were taking part.
Lithuania said it was eager to have Patriot missiles when the United States military displayed the system in the country earlier this month after using them in an exercise there.
"Under President Donald Trump, the United States will continue to hold Russian Federation accountable for its actions - and we call on our European allies and friends to do the same", Pence said Monday in Estonia. "The president has made that clear, had me make that clear when I visited South Korea earlier this year", Pence said.
Pence also tweeted Saturday night, along with a photo of himself boarding Air Force Two. As former U.S. ambassador to Russia Michael McFaul pointed out on NBC's Today show, it will also hurt Russia in other ways, such as applications for visas to travel to the US.
Pence's visit to Georgia is part of his three day tour to Estonia, Georgia and Montenegro in a clear message to Russian Federation that the change of power in the United States has not affected its stance toward allies across Eastern Europe anxious about Russia's growing assertiveness.