The measure is meant to punish Russian Federation for meddling in the 2016 USA election, its annexation of Ukraine's Crimea region and support for Syria's government in the six-year-long civil war.
The legislation would impose new sanctions against "corrupt Russian actors", "those involved in serious human rights abuses", Russians providing arms to Syrian President Bashar al-Assad's regime or those engaged in cyberattacks on behalf of the government.
The Senate said the new measures were meant to punish Moscow for Russia's violation of Ukraine's territorial integrity, cyberattacks and interference in the 2016 US elections.
Mueller is investigating alleged Russian interference in the 2016 U.S. presidential election and possible collusion with the Trump campaign.
The sanctions are in response to a trio of Russian actions, including their interference in the 2016 election, engagement in Syria and invasion of Crimea.
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Senior aides told Reuters they expected some sanctions package would eventually pass, but they expected the measure would be changed in the House.
The US Senate voted overwhelmingly on Thursday to approve sanctions against Russian Federation for its alleged interference in the 2016 election. In a statement, Sanders said that he opposed the bill not because of the new Russian Federation sanctions, which he supports, but because of the additional sanctions against Iran that were also part of the bill.
The measure also asserts a role for Congress if the White House opts to ease any sanctions against Moscow.
The Russian provisions would add people involved in the alleged Russian hacking attacks on the United States election to the sanctions list and impose penalties for delivery of weapons to the Syrian regime, hitting areas of the Russian economy such as mining and the energy sector.
The Russia sanctions measure was added as an amendment to an Iranian sanctions bill, after a deal was struck between the heads of the Senate Foreign Relations and Banking Committees.
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The penalties have been criticised by Austria and Germany for promoting USA economic interests.
"However, we can't accept the threat of illegal and extraterritorial sanctions against European companies", they said.
In a joint statement, Austria's Chancellor Christian Kern and Germany's Foreign Minister Sigmar Gabriel cited a section of the sanctions bill that calls for the United States to continue to oppose the Nord Stream 2 pipeline that would pump Russian gas to Germany beneath the Baltic Sea.
The only senators who voted against the measure were Republicans Rand Paul and Mike Lee.
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