Russian Prime Minister Dmitry Medvedev has said Donald Trump's signing of new sanctions on Russia is tantamount to a full-scale trade war.

Earlier Mr Trump signed off on legislation imposing further sanctions on Russia after the US Congress voted last week to punish the Russian government over interference in the 2016 presidential election, annexation of Ukraine's Crimea and other perceived violations of international norms.

Mr Trump, who has made clear he wanted to improve relations with Russia, grudgingly accepted the new congressional sanctions, which also included Iran and North Korea.

The bill had enough support in Congress to override a presidential veto.

Mr Trump called the legislation "significantly flawed" and urged Congress to not use the measure to hinder US efforts to resolve the Ukraine conflict with its European allies.

"While I favour tough measures to punish and deter aggressive and destabilising behavior by Iran, North Korea, and Russia, this legislation is significantly flawed," he said in a statement.

"In its haste to pass this legislation, the Congress included a number of clearly unconstitutional provisions."

However, he added that he was signing the bill "for the sake of national unity."

Responding to the sanctions, Mr Medvedev wrote in a Facebook post that in signing the legislation the Trump administration has shown it is utterly powerless.

He added that the sanctions mean an end to Russian hopes of better ties with the United States under Mr Trump.

White House adviser Kellyanne Conway confirmed the signing during an interview with Fox News.

Mr Trump's desire for better relations with Russia has been hamstrung by findings of US intelligence agencies that Russia interfered to help the Republican against Democratic presidential candidate Hillary Clinton.

US congressional panels and a special counsel are investigating.

Russia denies any meddling and Mr Trump denies any collusion by his campaign.

The Russian rouble weakened slightly following the initial report that Mr Trump had signed the bill.

European Commission President Jean-Claude Juncker has said the new sanctions had taken into account the bloc's concerns, but it stands ready to retaliate within days if the measures are applied to hurt its economic interests.

Mr Juncker said it was crucial to coordinate with the US to ensure sanctions against Russia over its role in the Ukraine crisis are effective.

Meanwhile Iran has said that the sanctions violate the nuclear deal between the two nations.

The ISNA news agency quoted Deputy Foreign Minister Abbas Araqchi as saying they will respond in an "appropriate and proportional" manner.