"If he does not, I will work with my colleagues to codify sanctions against Russia into law," McCain, chairman of the Senate Armed Services Committee and one of the Republican party's senior foreign policy voices, said in a statement.
A decision by Trump to ease sanctions imposed on Moscow over its annexation of Ukraine's Crimea region could complicate efforts to win Senate confirmation of Rex Tillerson, Trump's nominee for secretary of state.
Tillerson worked with Russia's government for years as a top executive at the energy giant Exxon Mobil, and has questioned the wisdom of sanctions against Russia that he said could harm U.S. businesses.
In 2013, Putin awarded Tillerson an Order of Friendship award for his work in Russia. Tillerson had engineered a joint venture with Russian oil companies estimated to be worth many billions of dollars.
Many senators, mostly Democrats but also Republicans such as McCain, Lindsey Graham and Marco Rubio, have expressed concerns about Tillerson becoming secretary of state because of his ties to Russia.
However, all three announced this week that they would support Tillerson, virtually ensuring he would become the top diplomat. A reversal by Trump of sanctions could turn lawmakers against him.