But the idea of Republican Trump wanting to strengthen the sanctions drew skepticism in Congress because his administration had spent weeks lobbying for a weaker bill. The sanctions, which the US House of Representatives has approved, need to pass in the Senate too before going to Trump's desk to sign or veto.
Trump's concerns include a provision letting Congress stop any effort to ease existing sanctions on Russia. But White House Communications Director Anthony Scaramucci suggested Trump in fact wanted stronger sanctions.
"He may sign the sanctions exactly the way they are or he may veto the sanctions and negotiate an even tougher deal against the Russians," Scaramucci told CNN.
Republicans and Democrats have pushed for more sanctions partly as a response to conclusions by US intelligence agencies that the Kremlin interfered in the 2016 presidential election campaign to help Trump.
Russian President Vladimir Putin, who has repeatedly denied meddling in the election, said Moscow would only decide on how to retaliate once it had seen the final text of the proposed law.
The bill would affect a range of Russian industries and might further hurt the Russian economy, already weakened by 2014 sanctions imposed after the Ukraine crisis.
Besides angering Moscow, the proposed legislation has upset the European Union, which has said the new sanctions might affect its energy security and prompt it to act, too.
On Wednesday, US lawmakers reached an agreement that cleared the way for the Senate to pass the measure as soon as this week.
The bill threatens to further derail US-Russian relations, which deteriorated under former President Barack Obama. Trump had hoped to improve ties but his administration has been clouded by investigations of Russian election meddling. Trump denies any collusion between his campaign and Moscow.
The sanctions bill also included new measures against Iran and North Korea.
"The message coming from Congress on a bipartisan basis is: These are hostile regimes, sanctions are warranted, sanctions are called for. And we want to make sure that they're tough sanctions, that they're endurable sanctions," said Republican U.S. House Speaker Paul Ryan, a Republican.
There was no definite word on when the Senate might vote on the bill but lawmakers said they thought a vote could be as soon as Friday. Senator Bob Corker, chairman of the Senate Foreign Relations Committee, said he hoped the bill would pass by unanimous voice vote.
"I would guess that he (Trump) will sign it," Corker told reporters.
Requesting anonymity to speak freely, both Republican and Democratic congressional aides scoffed at the suggestion that Trump would seek a 'stronger' deal. "It's bluster," one Democrat said.
White House spokeswoman Sarah Sanders said the Trump administration continues to support strong sanctions against Russia, North Korea and Iran, adding "we're going to wait and see what that final legislation looks like and make a decision at that point."
Trump can impose new sanctions at any time through an executive order.
"This bill doesn't preclude him from issuing tougher sanctions. That doesn't make any sense," said Edward Fishman, a former State Department official during the Obama administration who worked on US sanctions policy.
Putin said on a visit to Finland on Thursday that Russia was "exercising restraint and patience, but at some moment we'll have to retaliate. It's impossible to endlessly tolerate this boorishness towards our country."
Putin, at a joint news conference with Finnish President Sauli Niinisto, also spoke about Obama's order last December to seize Russian diplomatic property in the United States and to expel 35 Russian diplomats.
"This goes beyond all reasonable bounds," Putin said. "And now these sanctions - they are also absolutely unlawful from the point of view of international law."
Besides congressional probes, Special Counsel Robert Mueller is running a separate investigation. In lashing out against the investigation, Trump has criticized Attorney General Jeff Sessions, prompting speculation about Sessions' future.
Trump has also questioned Mueller's impartiality, leading to speculation he is the ultimate target. Republican Senator Lindsey Graham told CNN on Thursday he planned to introduce legislation to prevent improper firings of special counsels.
Asked if the US House of Representatives should act preemptively by passing legislation to prevent Trump from being able to fire Mueller without cause, Speaker Ryan said:
"I haven't given thought to that. I think it's in the president's interest that he stay where he is and that he continues and does his job."
The White House said in June Trump had no intention of firing Mueller.
(Reporting by Patricia Zengerle in Washington and Denis Pinchuk in Savonlinna, Finland; additional reporting by Susan Heavey, Eric Walsh, Rick Cowan, Valerie Volcovici, Roberta Rampton, Arshad Mohammed, Yeganeh Torbati, David Alexander and Doina Chiacu in Washington; Writing by Yara Bayoumy; Editing by James Dalgleish and Grant McCool)