After Moscow called the sanctions a declaration of "economic war" that had exposed the US president's weakness, an angry Trump lashed out at his own lawmakers who had overwhelmingly approved the measures.
"Our relationship with Russia is at an all-time & very dangerous low," Trump wrote on Twitter.
"You can thank Congress, the same people that can't even give us HCare!" he added in reference to a recent defeat in the Senate on his health care reform plans.
Senator John McCain, a noted Russia hawk, hit back on Twitter, suggesting Trump had misdiagnosed the source of the problem.
"Our relationship w/ Russia is at dangerous low. You can thank Putin for attacking our democracy, invading neighbors & threatening our allies," McCain said.
Trump's outburst came a day after he grudgingly signed off on the sanctions, calling the legislation "significantly flawed" and adding that some of its provisions were unconstitutional.
Trump's presidency has been overshadowed by allegations that his team colluded with Moscow during last year's US presidential campaign in which he defeated Hillary Clinton.
On Thursday, reports emerged that special investigator Robert Mueller had impaneled a grand jury to investigate the issue, a step toward possible criminal indictments.
The move is a sign that the sweeping federal investigation -- which includes allegations that Trump campaign officials coordinated with Russia to tilt the election in the Republican's favor -- is gathering pace.
After meeting his Russian counterpart Vladimir Putin at a G20 summit in Germany last month, Trump said he wanted to work more closely with Moscow on areas such as the conflict in Syria.
Special investigator and former FBI Director, Robert Mueller (Getty Images). Source: Getty Images
But the sanctions law -- which also includes measures against North Korea and Iran -- greatly limits his room for maneuver and underlines the lack of trust from lawmakers, even though his Republican Party controls both houses of Congress.
The sanctions target the Russian energy sector in particular, giving Washington the ability to sanction companies involved in developing Russian pipelines.
The measures also place curbs on some Russian weapons exporters and constrain Trump's ability to waive the penalties.
Moscow, which announced a series of retaliatory measures over the weekend, has painted the bill's passage in the Senate as a humiliation for Trump.
Prime Minister Dmitri Medvedev took to Facebook late Wednesday to say Trump's signing of the bill "ends hopes for improving our relations with the new US administration."
"It is a declaration of a full-fledged economic war on Russia," Medvedev wrote.
"The Trump administration has shown its total weakness by handing over executive power to Congress in the most humiliating way."
Moscow has already ordered the US to slash diplomatic staff in Russia by 755 personnel in response.
Russian President Vladimir Putin (R) and Prime Minister Dmitry Medvedev (L) attends the Supreme State Council of Russia (Getty Images). Source: Getty Images
The Kremlin said Trump's formal approval did not "change anything" and no further retaliation was planned.
The head of Russia's largest oil firm Rosneft -- which has already been targeted by earlier US sanctions imposed over the Ukraine crisis -- promised the company would try to avoid more pain.
"We will seek to work in such a way as to minimize the impact of the sanctions," Igor Sechin told Russian news agencies, adding that sanctions had "started backfiring" to damage American interests.
Iran reacted angrily, saying the new sanctions against it "violated" its 2015 nuclear deal with world powers, and warned it would respond "appropriately."
The sanctions seek to penalize the Kremlin for allegedly meddling in the 2016 US presidential election and for Russia's annexation of Crimea.
Washington has already slapped several rounds of sanctions on Moscow over Ukraine since 2014, and in December, then leader Barack Obama turfed 35 Russian diplomats out due to accusations of election interference.
Trump had received the legislation at 1:53 pm on Friday, but waited until Wednesday to sign it.
The delay had raised speculation that Trump might veto or try to somehow shelve the sanctions, which were approved in a 98-2 Senate vote.
By signing it, he avoided the humiliating prospect of Congress overriding his veto.
US Secretary of State Rex Tillerson said Wednesday that he would meet with his Russian counterpart Foreign Minister Sergei Lavrov over the weekend, but warned US-Russia ties could still get worse.
