Russia has retaliated to tough new sanctions proposed by the US Senate, ordering Washington to reduce its diplomatic staff in Moscow.

In a statement on Friday, Russia's foreign ministry said the United States must reduce its staff to 455 people by September 1. It added that it was seizing a compound and warehouse used by US diplomats.

"We propose to the US side to bring the number of diplomatic and technical staff working in the US embassy in Moscow and the consulates general ... in exact accordance with the number of Russian diplomats and technical staff in the US," the statement said.

The sanctions, outlined in a new bill passed on Thursday, violated international law and demonstrated "extreme aggression of US in international affairs", Russia said.

It also warned the US it would respond in kind if Washington decided to expel any Russian diplomats.

The sanctions against Moscow are punishment for its alleged meddling in the 2016 presidential election and its military actions in Ukraine and Syria.

According to the bill, US President Donald Trump would be barred from easing the Russia sanctions without first getting permission from Congress, a demand that could imperil his bid for better relations with Moscow.