The Senate is poised to assist President Donald Trump in applying pressure on Moscow, despite the administration's hope for a ceasefire agreement.
"We also stand ready to provide President Trump with any tools he needs to get Russia to finally come to the table in a real way," Thune said during a Senate session.
He later informed reporters of his discussions with the White House regarding the sanctions bill.
The proposed measures include a 500% tariff on nations purchasing Russian oil, gas, uranium, and other exports.
China and India account for about 70% of Russia's international energy trade, which funds its war effort.
The bill, primarily authored by Republican Senator Lindsey Graham of South Carolina and Democratic Senator Richard Blumenthal of Connecticut, currently has at least 82 co-sponsors in the Senate.
"I think right now they're still hopeful they'll be able to strike some sort of a deal," Thune said.
“But as you might expect, there's a high level of interest here in the Senate, on both sides of the aisle, and moving on it, and it very well could be something that we would take up in this work period.”
Lawmakers leave Washington for the Independence Day recess on July 4.
Reuters highlights this as a rare example of bipartisanship in the often-divided U.S. Congress, noting Trump's growing impatience with the delay in reaching a peace agreement with Moscow.
To become law, the bill must pass both the Senate and the House of Representatives and be signed by Trump. However, he has expressed concerns that new sanctions might harm the prospects for a peace agreement.
Meanwhile, Republican leaders in the House have shown no signs of planning a vote on the sanctions package.
Bill on sanctions against Russia in the U.S. Senate
On April 1, The Washington Times reported that a new sanctions bill was introduced in the U.S. Senate, proposing a 500% tariff on imports from countries continuing to purchase Russian oil and raw materials.
The measures are designed to increase economic pressure on Russia and create additional obstacles for countries trading in Russian energy resources.
With over 70 senators reportedly supporting the bill, it demonstrates a strong bipartisan consensus.
On May 20, U.S. Secretary of State Marco Rubio warned that additional sanctions threats could deter Russia from peace talks.
However, Senator Graham reiterated the Senate's readiness to vote on the sanctions bill if progress in negotiations over Russia's war against Ukraine is not forthcoming. On May 27, Graham published an op-ed in The Wall Street Journal, reaffirming the Senate's commitment to imposing 500% tariffs on countries purchasing Russian energy.