Kremlin spokesman Dmitry Peskov. AFP/Kirill Kudryavtsev

MOSCOW: The Kremlin said Wednesday that US President Donald Trump signing new sanctions against Russia into law "doesn't change anything" as Moscow has already hit back at Washington over the latest moves.

"De-facto this doesn't change anything," Kremlin spokesman Dmitry Peskov told Russian news agencies, adding that "retaliatory measures have already been taken".

Trump reluctantly approved new sanctions against Russia Wednesday, bowing to domestic pressure and putting efforts to improve ties with the Kremlin on the ice.

The US president signed the legislation behind closed doors and away from the cameras, after failed efforts to scupper or water down the bill.

Trump's reluctance was on full display in an angry signing statement, in which he called the legislation "significantly flawed".

Expecting the signature, Russia on Friday preemptively struck back against the measures after they were approved overwhelmingly by the US Senate.

Moscow has ordered Washington to slash its diplomatic mission in Russia by 755 staff and blocked two embassy compounds.

US Secretary of State Rex Tillerson said Tuesday he will meet with his Russian opposite Foreign Minister Sergei Lavrov over the weekend, but warned that US-Russia ties could still get worse.