He noted that he and Senators Blumenthal and Shaheen worked closely to ensure the language was acceptable to the executive branch.
"I've never been more optimistic than I am today," said Graham.
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He added that the strategy involves making Ukraine more lethal while establishing consequences for nations supporting Russia.
"We have the formula to end this war. Help Ukraine be more lethal.
Let those supporting Russia know it's going to be a price to be paid if you keep doing it.
And try to find an off-ramp, not to humiliate Putin, but to end this war so that Ukraine will thrive and survive," said Graham.
The agreement follows a recent meeting between President Donald Trump and Zelenskyy at the NATO summit in Ankara, marking a shift from their tense February 2025 Oval Office meeting.
"We've actually developed a good relationship," said Trump during the Ankara meeting.
He noted the contrast from their previous discussions, stating the relationship had improved dramatically.
"It's hard to believe, right? From the Oval Office to now, I think we've developed a very good relationship," said Trump.
Senior US officials stated on July 10 that Trump supports the updated sanctions legislation, which Senate Majority Leader John Thune had previously delayed.
Ukrainian officials welcomed the congressional progress, citing the critical nature of restricting Moscow's energy revenues.
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"Russia has earned roughly $58 billion from oil and petroleum product exports to China and India in the first half of this year alone," said Vladyslav Vlasiuk, Zelenskyy's commissioner for sanctions policy, to RFE/RL on July 10.
