"The hope of improving our relations with the new U.S. administration has come to an end," said Medvedev on Facebook, commenting on the signing of the bill by U.S. President Donald Trump.
The bill was approved overwhelmingly early this month by the U.S. Congress despite the Trump administration calling on lawmakers to grant the White House "flexibility" in dealing with Russia.
The Trump administration demonstrated "complete impotence, in the most humiliating manner, transferring executive powers to Congress," said Medvedev.
"The U.S. establishment completely outplayed Trump. The president is not happy with the new sanctions, but he can not refuse to sign the law," said the Russian prime minister.
According to him, the interests of U.S. businesses are almost ignored, and anti-Russian hysteria has become a key part of U.S. foreign and domestic policy.
The sanction regime is codified and will last for decades as the new law allows the Congress to limit the president's power to lift anti-Russian measures, said Medvedev.
"Therefore, the relationship between Russia and the United States will be extremely tense, regardless of the composition of the Congress or the personality of the president," he said.
Against such a backdrop, Russia will continue to work quietly on economic and social development, count primarily on itself and reduce reliance on imports from the West, he said.
Also on Wednesday, the Russian Foreign Ministry regretted the enactment of the bill and blasted the new sanctions as "short-sighted and even dangerous."
Nevertheless, the ministry said in a statement that Russia remains open to cooperation with the United States in various areas, including on the settlement of regional conflicts.
"However, fruitful cooperation is possible only if U.S. politicians overcome their own delusions and cease to perceive the world around them through a reality-distorting prism of 'American exclusiveness,'" said the ministry.
In retaliation for the new U.S. sanctions, Russian President Vladimir Putin on Sunday announced a decision to reduce the U.S. diplomatic staff in Russia by 755 people by Sept. 1.
"Naturally, we reserve the right to take additional countermeasures," said the foreign ministry statement.