United States President Donald Trump has grudgingly signed into law fresh sanctions against Russia that Congress had overwhelmingly approved last week, criticising the legislation as having "clearly unconstitutional" elements.

Key points: The sanctions are the first major foreign policy legislation since Mr Trump took office

The sanctions are the first major foreign policy legislation since Mr Trump took office Mr Trump says the sanctions bill is "flawed" and "unconstitutional"

Mr Trump says the sanctions bill is "flawed" and "unconstitutional" The new measures allow Congress to stop attempts by Mr Trump to ease sanctions

After signing off on sanctions that seemed to run counter to his desire to improve relations with Moscow — but which also affect Iran and North Korea — Mr Trump laid out a lengthy list of concerns.

"While I favour tough measures to punish and deter aggressive and destabilising behaviour by Iran, North Korea, and Russia, this legislation is significantly flawed," Mr Trump said in a statement announcing the signing.

The Republican-controlled Congress approved the legislation by such a large margin on Thursday that it would have thwarted any effort by Mr Trump to veto the bill.

The legislation has already provoked countermeasures by Russian President Vladimir Putin, who has ordered big cuts to the number of staff at the US diplomatic mission to Russia.

Congress approved the sanctions to punish the Russian Government over interference in the 2016 presidential election, the annexation of Ukraine's Crimea, and other perceived violations of international norms.

Space to play or pause, M to mute, left and right arrows to seek, up and down arrows for volume. Watch Duration: 7 minutes 42 seconds 7 m Interview: Ben Kamisar, US Political reporter

Mr Trump said he was concerned about the sanctions' effect on work with European allies, and on American business.

"My administration … expects the Congress to refrain from using this flawed bill to hinder our important work with European allies to resolve the conflict in Ukraine, and from using it to hinder our efforts to address any unintended consequences it may have for American businesses, our friends, or our allies," he said.

The President also complained about what he said were "clearly unconstitutional provisions" in the legislation relating to presidential powers to shape foreign policy.

Relations are 'going to be extremely tense'

Moscow had initially hoped that Mr Trump would work to repair the US-Russia relationship. ( AP: Evan Vucci )

Russian Prime Minister Dmitry Medvedev was quick to castigate Mr Trump for his "humiliating" concession to Congress, saying the move would have "a few consequences".

"First, it ends hopes for improving our relations with the new US administration," he said.

"Second, it is a declaration of a full-fledged economic war on Russia.

"Third, the Trump administration has shown its total weakness by handing over executive power to Congress in the most humiliating way.

"This changes the power balance in US political circles."

Mr Medvedev said relations between the two countries would become "extremely tense" and that Mr Trump had been knocked "down a peg" by Congress.

"The US establishment fully outwitted Trump; the President is not happy about the new sanctions, yet he could not but sign the bill," he said.

"The issue of new sanctions came about, primarily, as another way to knock Trump down a peg.

"New steps are to come, and they will ultimately aim to remove him from power."

New bill limits Trump's powers to ease sanctions

The new sanctions measure, the first major foreign policy legislation approved by Congress since Mr Trump took office in January, includes a provision allowing Congress to stop any effort by the President to ease existing sanctions on Russia.

Mr Trump has long said he would like improved ties with Russia. But any such efforts by his administration have been hamstrung by findings by US intelligence agencies that Russia interfered to help the Republican against Democratic presidential candidate Hillary Clinton.

US congressional committees and a special counsel are investigating. Moscow denies any meddling and Mr Trump denies any collusion by his campaign.

In a second statement on the legislation, Mr Trump said that, "Despite its problems, I am signing this bill for the sake of national unity."

"It represents the will of the American people to see Russia take steps to improve relations with the United States."

But he said the law was "seriously flawed — particularly because it encroaches on the executive branch's authority to negotiate".

The legislation will affect a range of Russian industries and might further hurt the Russian economy, already weakened by 2014 sanctions imposed after Russia annexed Crimea from Ukraine.

It also cracks down on Iran and North Korea for activities that include their missile development programs and human rights abuses, including seeking to punish foreign banks that do business with North Korea.

'Retaliatory measures already taken': Kremlin

After Congress approved the sanctions, the Kremlin ordered the United States to cut about 60 per cent of its diplomatic staff in Russia.

Mr Putin said on Sunday that Russia had ordered the US to cut 755 of its 1,200 embassy and consulate staff by September, and was seizing two diplomatic properties.

Responding to Mr Trump's signing of the new bill, the Kremlin responded that it had already taken retaliatory measures, citing the expulsion of US diplomatic staff from Moscow.

"What retaliatory measures?" Kremlin spokesman Dmitry Peskov said.

"There is nothing new. Retaliatory measures were already taken."

Besides angering Moscow, the legislation has upset the European Union, which has said the new sanctions might affect its energy security and prompt it to act, too.

The legislation would give the Trump administration the option of imposing sanctions on companies helping develop Russian export pipelines, such as the Nord Stream 2 pipeline carrying natural gas to Europe, in which German companies are involved.

US diplomatic properties in Russia were evacuated earlier this week. ( Reuters: Tatyana Makeyeva, file )

Reuters