It now heads to the Senate before Trump faces the tricky choice of whether to veto the bill, which has been opposed by the White House...
The package, which targets Russia, Iran and North Korea, "tightens the screws on our most dangerous adversaries in order to keep Americans safe," House Speaker Paul Ryan said after it passed on Tuesday by 419 votes to three.
It now heads to the Senate before Trump faces the tricky choice of whether to veto the bill, which has been opposed by the White House and considerably constrains his ability to lift the penalties.
While Moscow and Tehran raised the prospect of retaliation over any fresh punitive measures, the EU also warned it was "ready to act to protect European interests" if the legislation hit dealings with the Russian energy sector.
The US bill was the result of a congressional compromise aimed at punishing the Kremlin for allegedly interfering in the 2016 US presidential election and intervening in Ukraine.
Key among the provisions is one that handcuffs Trump by complicating any unilateral efforts to ease santions against Moscow in future -- effectively placing him under Congress's watch.
"Left unchecked, Russia is sure to continue its aggression," House Foreign Affairs Committee chairman Ed Royce said, applauding the bill's backing.
Despite initially opposing the bill, Trump appears to have few options in the face of near-total consensus in Congress, with a decision likely due by mid-August.
Spokeswoman Sarah Huckabee Sanders said the White House was still "reviewing the House legislation and awaits a final legislative package for the president's desk".
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 each chamber.
Moscow responded angrily to the vote, with deputy foreign minister Sergei Ryabkov insisting Washington had been warned "dozens of times" that any new sanctions would "not go unanswered".
"The authors and sponsors of this bill are taking a very serious step towards destroying the possibilities for normalising relations with Russia," he told state-run TASS news agency.
Ties between Moscow and Washington have been at their lowest point since the Cold War since the US began slapping sanctions on Russia after its annexation of Crimea in 2014.
Trump repeatedly pledged to improve relations during his campaign, raising the prospect that he could roll back the Obama-era punishments.
Since then, accusations from US intelligence that the Kremlin meddled in the vote to get Trump elected have made any softening of the stance on Russia politically toxic.
The bill also includes fresh sanctions against Iran and its Islamic Revolutionary Guard Corps, which stands accused of supporting terrorism, and North Korea, for its missile tests, are also included.
Iranian President Hassan Rouhani said Tehran would respond in kind to any breach by the US of the 2015 nuclear deal after the vote.
The Iranian parliament's national security and foreign affairs committee said it would hold an extraordinary session on Saturday to discuss its response.
In a rare feat, the US vote has also managed to upset European Union nations worried that it could damage their energy interests.
European commissioners, the EU executive's top officials, "expressed their concerns notably because of the draft bill's possible impact on EU energy independence," the bloc said in a statement following talks in Brussels on Wednesday.
In an apparent concession, the House modified a provision so the bill only targets pipelines originating in Russia, sparing those that merely pass through, such as the Caspian pipeline that carries oil from Kazakhstan to Europe.
But Brussels worries that the fresh wave of measures could end up penalising European firms that contribute to the development of Russia's energy sector.
"Depending on its implementation, this could affect infrastructure transporting energy resources to Europe," including those transiting through Ukraine, the EU said in a statement.
Brussels also decried the sanctions bill as a unilateral action by Washington that disrupted previous close cooperation on measures against Russia, which took a toll on its economy.
The EU and US imposed the punishment after Russia's annexation of Crimea, before Moscow was later accused of backing a separatist insurgency to halt Ukraine's pivot to the West.
The two sides later imposed broader economic sanctions after the shooting down of Malaysia Airlines flight MH17 in July 2014, which international investigators say was downed by a Russian missile fired from rebel-held territory.