In particular, the law imposes sanctions against Russia's defense, intelligence, mining, shipping and railway industries and restricts dealings with Russian banks and energy companies.
On Wednesday, the White House also issued a statement in which the president described the newly signed law as "seriously flawed" since "it encroaches on the executive branch’s authority to negotiate."
Commenting on the statement, Rep. Senator John McCain said that Trump’s concerns were "misplaced."
"The concerns expressed in the president’s signing statement are hardly surprising, though misplaced," McCain said Wednesday.
'Hostage of Congressional Opinion'
A day after he signed the law, Trump said that relations between Washington and Moscow are at "an all-time and very dangerous low" and cast the blame on Congress.
"Our relationship with Russia is at an all-time & very dangerous low. You can thank Congress, the same people that can't even give us HCare!" Trump said in a Twitter statement on Thursday.
Meanwhile, some experts pointed out that Trump is getting increasingly dependent on the establishment and Congress limits his actions.
"The US ruling elite demonstrates that they will not let him [Trump] carry out the policy towards Russia he initially planned. This is weakening Trump’s power and his ability to make decisions," Pushkov told journalists.
According to him, currently Congress plays the leading role in making decisions on US-Russia relations. The new sanctions law delivered a heavy blow to bilateral ties, especially amid the ongoing scandal over diplomatic property. The lawmaker added that Syria remains the only matter on which Moscow and Washington can continue to cooperate.
Russia Will Continue Talks With Trump
"I can’t see any insurmountable tensions between Trump and Congress. This standoff is not serious, it is rather about rhetoric," Bruter told RT.
According to the analyst, Trump is not giving in to congressional pressure and will continue to defend his positions at any expense.
"I guess that Trump will fight. There is no coincidence that he has paid so much attention to sanctions. He will try to convince lawmakers that they interfere with his policy. The US would win if the president’s hands were untied," Bruter suggested.
He added that despite the persisting differences between the White House and Congress, Trump continues to remain the "main negotiator" on the issues concerning US-Russia ties. Moscow will continue a dialogue with Washington, taking into account the tensions between Trump and Congress.
"It is necessary to talk to Trump and [US State Secretary Rex] Tillerson. Moscow cannot ignore such an opportunity. The question is whether these negotiations will be productive or not," Bruter said.
'Bound Hand and Foot'
He said that usually there is such a standoff if the president and Congress rival political forces. But the current "Republican-dominated Congress is trying to bind the hands and feet of the Republican president."
According to Suchkov, if Congress stays too focused on internal political struggles this will reduce the Republican Party’s chances for the 2018 election.
"As a result, the Democrats would have the chance to win a majority. If real, such a scenario may pave the way for Trump’s impeachment," the expert suggested.
At the same time, the analyst said that Trump has already blamed the decision on Congress, in an attempt to avoid responsibility. Suchkov suggested that Trump and his administration would continue to use this argument at their talks with Moscow.
Commenting on the prospects on US-Russia talks, the expert underscored that expectations should be "sober and cautious."
"The fact that the US continue to cooperate with Russia on Syria is positive. But Moscow should not expect major joint projects and any serious deals with Washington," Suchkov concluded.