The legislation, which is the result of a congressional compromise reached at the weekend and is aimed at punishing the Kremlin for meddling in the 2016 US presidential election.
The legislation, which is the result of a congressional compromise reached at the weekend and is aimed at punishing the Kremlin for meddling in the 2016 US presidential election and Russia's annexation of Crimea, could end up penalizing European firms that contribute to the development of Russia's energy sector.
New sanctions against Iran and North Korea for their actions on or testing of ballistic missiles are also included in the bill.
Key among the provisions is one that handcuffs the US president by making it difficult for him to unilaterally ease penalties against Moscow in the future -- effectively placing him under Congress's watch.
Initially, Trump resisted the legislation. But faced with near-total consensus among Republican and Democratic lawmakers, the White House blinked.
In mid-June, the Senate voted 98-2 in favor of tough sanctions on Moscow and Tehran, but the text stalled in the House.
Now that an agreement was reached Saturday, the House vote could be similarly overwhelming.
The measure would then return to the Senate for final passage, likely before summer break in mid-August.
The bill includes sanctions against Iran and its Islamic Revolutionary Guard Corps, which stands accused of supporting terrorism, and North Korea, for its missile tests.
"I am pleased to see the Congress work as a whole to hold Iran, Russia, and North Korea accountable for their continued destabilizing activities across the world," Democratic Senator Robert Menendez said in a statement.
The bill also "sends a clear message to the president that Congress is prepared to act with a united voice," he added.
While the commander in chief has called for improved relations with Russia and President Vladimir Putin, the White House has said Trump backs sanctions on Russia.
But it did not say directly that Trump would sign the bill.
"He's going to study that legislation and see what the final product looks like," spokeswoman Sarah Sanders told reporters Monday on Air Force One.
US lawmakers, including Republican leaders, have remained wary of the intentions of the billionaire businessman-turned-president regarding a relaxation of pressure on Putin.
Even if Trump ended up vetoing the legislation, Congress would likely be able to overcome such a blockage with a two-thirds majority in each chamber.
The Kremlin on Monday warned that fresh sanctions on Russia would hit the interests of both sides.
"We consider such a continuation of the rhetoric of sanctions counter-productive and harmful to the interests of both countries," Kremlin spokesman Dmitry Peskov said.
From Paris to Berlin the sanctions bill was seen as Washington's unilateral action that disrupts a carefully crafted order.
To date, sanctions against Russia have been coordinated on both sides of the Atlantic, so the Western bloc appeared united.
"For us, G7 unity regarding sanctions is of key importance as it is the respect of implementation of Minsk agreement," European Commission spokesperson Margaritis Schinas said.
Commission President Jean-Claude Juncker has signalled that the European Union would be prepared to respond.
Several European nations including Germany are livid because the new law would allow the punishment of companies engaged with pipelines from Russia, for example by limiting their access to US banks.
The provision could theoretically pave the way for sanctions against the European partners in Nord Stream 2, a project to build a pipeline carrying Russian gas across the Baltic which could boost supplies to Germany from 2019.
Such partners include France's Engie, Germany's Uniper and Wintershall, Austrian firm OMV and the Anglo-Dutch Shell.
To date, Washington and Brussels had agreed that sanctions would not affect Europe's gas supply.
In an apparent concession, the House slightly modified a provision so that the bill only targets pipelines originating in Russia, sparing those which merely pass through Russia, such as the Caspian pipeline which carries oil from Kazakhstan to Europe.