Sergei A. Ryabkov, the Russian deputy foreign minister, said that the new sanctions would bury any prospect of improving relations, calling the measures “beyond common sense.”

“The authors and sponsors of this bill are making a very serious step toward destruction of prospects for normalizing relations with Russia and do not conceal that that’s their target,” Mr. Ryabkov said, according to the Russian news agency Itar-Tass. Despite that, he added, Moscow remained ready to cooperate on shared concerns, including fighting terrorism.

Last December, former President Barack Obama ordered the expulsion of 35 Russian diplomats and the closing of two Russian diplomatic estates near Washington and New York. Mr. Putin, anticipating better relations under a Trump administration, did not respond at the time. Many say they believe the Russian leader’s most likely first step will mirror those actions, and Moscow has been threatening to take such measures for weeks.

The American bill, passed by a vote of 419 to 3 by the House of Representatives on Tuesday, bolsters economic sanctions against Russia that were imposed after Moscow annexed Crimea and destabilized Ukraine in 2014.

The measures reflect Congress’s growing unease with Mr. Trump’s relatively warm attitude toward Russia despite repeated assertions from United States intelligence agencies that Moscow hacked the American election. The law would require Mr. Trump to seek congressional approval before lifting any sanctions — a curb on executive authority that has prompted mixed signals from the White House about whether Mr. Trump will sign any final version of the bill.

Russia, effectively ignoring the fact that its election meddling had prompted the measures, used the push for tightened sanctions as further proof that deep forces in the American government were continuing to thwart Mr. Trump’s wish, expressed during the campaign, to improve ties with Moscow.

Mr. Trump will sign the bill because he is “a prisoner of Congress and anti-Russian hysteria,” Aleksei K. Pushkov, another Russian legislator and frequent commentator on foreign relations, wrote on Twitter. He called the sanctions “a new stage of confrontation” and mused whether the restaurant chain McDonald’s should be targeted in response.