Pence said he had passed on a "simple message" from President Donald Trump to the three countries: "We are with you."
"We hope for better days, for better relations with Russia but recent diplomatic action taken by Moscow will not deter the commitment of the United States of America to our security, the security of our allies and the security of freedom loving nations around the world," Pence said in Estonia after meeting with the leaders of the three Baltic states.
At a news conference, Pence said he had passed on a "simple message" from President Donald Trump to the three countries: "We are with you."
President Vladimir Putin on Sunday said the United States would have to cut 755 diplomatic staff in Russia and warned of a prolonged gridlock in its ties after the US Congress backed new sanctions against the Kremlin.
Putin added bluntly that Russia was able to raise the stakes with America even further, although he hoped this would be unnecessary.
Estonia, where Pence had on Sunday raised the possibility of deploying the Patriot anti-missile defence system, is the first stop of his European tour which will also take him to Georgia and Montenegro.
The aim of the trip is to reassure America's allies who say they are worried by Russian expansionism.
"We stand with the people and nations of Estonia, Latvia and Lithuania and we always will," Pence said.
A "strong and united NATO" was important, as Russia continued "trying to redraw borders", he said.
"The US will check any attempt to use force," Pence said.
The US government hoped for a better relationship with Russia, but stood by the NATO treaty's article 5 on collective defence. "An attack on one of us is an attack on us all," he said.
Pence also said that exports of US liquid natural gas to the Baltic states, which have already started, "will contribute to prosperity and security" in the three countries which are still heavily dependent on Russian gas.
Pence is scheduled to address NATO troops deployed in Estonia before travelling on to Tbilisi.