Trump reluctantly signed off on the new sanctions Wednesday, bowing to domestic pressure after the White House failed to scupper the bill or water it down.
Medvedev warned the move would have "consequences", saying "it ends hopes for improving our relations with the new US administration."
"Second, it is a declaration of a full-fledged economic war on Russia," Medvedev said on his Facebook page.
Trump signed the legislation behind closed doors and his reluctance was on full display in an angry signing statement in which he called the legislation "significantly flawed."
"In its haste to pass this legislation, the Congress included a number of clearly unconstitutional provisions," he said, including curbs on the president's ability to "negotiate" with Russia.
"I built a truly great company worth many billions of dollars. That is a big part of the reason I was elected. As president, I can make far better deals with foreign countries than Congress," Trump claimed.
Iran, too, reacted angrily, saying the new sanctions against it "violated" its 2015 nuclear deal with world powers, and warned it would respond "appropriately."
With regards to Russia, the sanctions notably constrains Trump's ability to waive the penalties - a statement of mistrust from the Republican-controlled Congress, which remains unsettled by Trump's warm words for President Vladimir Putin.
In his statement, Trump said: "The Framers of our Constitution put foreign affairs in the hands of the President. This bill will prove the wisdom of that choice."
"I hope the president will be as vocal about Russia's aggressive behaviour as he was about his concerns with this legislation."
The sanctions seek to penalise the Kremlin for allegedly meddling in the 2016 US presidential election and for Russia's annexation of Crimea.
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