The Kremlin responded coolly to the sanctions vote, saying that President Vladimir Putin would wait for the approval by the US Senate, the final step necessary before the law goes for signature by US President Donald Trump.
The sanctions were approved in a landslide yesterday by the US lower house despite the initial opposition of Trump who came to office on a pledge to mend ties with the Kremlin.
"If our concerns are not taken into account sufficiently, we stand ready to act appropriately within a matter of days. America first cannot mean that Europe's interests come last," European Commission head Jean-Claude Juncker said.
"The US bill could have unintended unilateral effects that impact the EU's energy security interests," added Juncker, saying that there should be unity among western allies on sanctions.
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The row comes just a day after Trump blasted the "very protectionist" EU's trade policies, saying Washington was working on a deal with Britain after Brexit.
The latest US sanctions package is aimed at punishing the Kremlin for allegedly meddling in the 2016 US presidential election, and Russia's annexation of Crimea.
The EU is worried the sweeping measures would still unfairly penalise European firms that contribute to the development of Russia's energy sector, and its diplomats have heavily lobbied Washington to water down the measures.
However France said the US bill was "illegal" in terms of international law, in its current form, according to a foreign ministry spokeswoman said.
Germany believed that "European businesses must not be targeted by the US sanctions", government spokeswoman Ulrike Demmer said.
But Berlin -- which led efforts against the bill amid fears it would hit a controversial pipeline project between Russia and Germany known as Nord Stream 2 -- also insisted the legislation had been modified to require that Washington confer with EU allies if the sanctions should involve the European energy supply.
But other projects are at risk, with major energy companies such as Italy's ENI, Shell and BP all crying out for a halt to the sanctions.
"It seems that we energy companies are nothing but ping pong balls... In a political game," Mario Mehren, CEO of German firm Wintershall told Russian news agency RIA Novosti.
The EU and US imposed sanctions in the wake of Russia's annexation of Crimea in March 2014, overcoming division on how far to go in punishing Moscow.
The Kremlin initially slammed the vote as a "serious step" towards wrecking chances of improving US-Russia ties just weeks after Putin and Trump held their first face to face meeting in Germany.
But it later took a softer tone.
"For now we are still only talking about a bill so we won't give any substantive evaluations," Kremlin spokesman Dmitry Peskov said. "Let's wait for this legislation to become law."
With Trump caught up in a deep scandal about alleged links to Russia, the tycoon appears to have few options but to sign the law in the face of near-total consensus in Congress. A Senate vote is likely due by mid-August.
But even if Trump were to veto the legislation, Congress would likely be able to overcome such a blockage with a two- thirds majority in both the House and the Senate.
The new US sanctions also target Iran and North Korea, with Iranian President Hassan Rouhani promising to respond in kind to any breach to the 2015 nuclear deal, under which the country agreed to wind down its nuclear programme in exchange for an easing of Western sanctions.