A vote on the bill is expected in the coming weeks, after which it will land on the president's desk for signing.
According to a memo obtained by the Financial Times, Brussels is preparing to retaliate "within days" if Washington adopts its new "unilateral" sanctions against Russia without taking EU interests into account.
In an interview with Sputnik, Russian security expert Dmitry Danilov said, "Trump immediately made it clear that he will formulate the rules of the game," and that "he is not too inclined to initially meet Europe's interests."
"His positions were quite tough and categorical, and this could be seen during all his meetings," Danilov said, adding that Europeans were especially hit by the US leader's refusal to join the Paris agreement on climate.
Danilov recalled that under the Obama administration, Russia was seen as the main challenge to European security, while Trump calls for concentrating on combating terrorism, a task that cannot be resolved without Russia.
"The Europeans who supported Obama's hardline stance on Russia now got into a strange situation, when the current US leader actually turned or is ready to turn in the opposite direction," Danilov said.
"Therefore, the issue of sanctions is now considered in the context of Trump's independence, readiness and ability to uphold his own political line," said Danilov.
According to him, the European Union (EU) has already realized the fact that it needs to rely more on itself.
"Despite the fact that their significant dependence on the United States is still in place, it is time that they formulate their own position and pursue their own policies," Danilov said, urging the EU to seize the new opportunities amid the change of political elites in Europe.
Danilov did not rule out that the EU will continue to formulate tough responses to the US's anti-Russian sanctions, but it will be difficult for Brussels to stick to the sanctions if they are applied.
"In order to abandon sanctions, it is necessary to adopt another political decision by the consensus of European countries, which is an impossible task. On the contrary, this consensus and this political position now just boils down to supporting the sanctions," he said.
He added that the EU will not be able to obtain guarantees from the US that European interests will not be affected "because the issue will be moved to the legislative field."
White House press secretary Sarah Huckabee Sanders told reporters on Sunday that the White House supported the "tough on Russia" approach of the new bill, adding that President Donald Trump was intent on signing it.
The new sanctions include restrictions in the energy sector, and specifically target the Nord Stream 2 project, a joint venture involving Russian energy giant Gazprom and energy companies from Germany, France, Austria, the Netherlands and the UK to bring Russian natural gas to Western Europe via a pipeline in the Baltic Sea.
The bill explicitly threatens to target European companies working with Russia on the project, leading to consternation in Brussels.