The House-approved bill includes a provision attached to Russian measures that would require Congress to approve waivers sought by the US president on specific items.
"We have certain concerns about the reach into the executive powers and certain limitations," Mnuchin told the Senate Appropriations Subcommittee on Financial Services and General Government. "But we fully support sanctions on North Korea, on Russia, on Iran."
When asked whether President Donald Trump would sign the bill, which has yet to clear the US Senate, Mnuchin replied that he did not know because he has not spoken with Trump.
The measures against Russia stem from charges that Moscow meddled in the 2016 US presidential election.
Russia has repeatedly refuted the US allegations that it interfered in the 2016 election, calling them absurd and intended to deflect public opinion from actual election fraud and corruption as well as other pressing domestic issues.
The Senate is not expected to take up the sanctions legislation until after the August recess.