Graham made these demands while responding to comments from Vice President Kamala Harris at the Munich Security Conference in Germany, where she said that the United States has formally determined that Russia has committed crimes against humanity in Ukraine.
According to Graham, it is insincere for Harris to talk about Russia perpetrating crimes against humanity while refusing to support Ukraine with even more advanced weapons systems, including American combat aircraft. (Related: Matt Gaetz introduces House resolution urging Biden to end all taxpayer-funded aid for Ukraine.)
"How can she say that – and she is correct – and not give the victim of the crime against humanity the defensive weapons they need to stop the crime?" he said.
"You label Putin's Russia as a state sponsor of terrorism [and] you create international tribunals so we actually can try [Russian President Vladimir] Putin and his cronies in the international court like we did after World War II," said Graham during an interview.
"So we need to do two things quickly: Make Russia a state sponsor of terrorism under U.S. law, which would make it harder for China to give weapons to Russia, and we need to start training Ukrainian pilots on the F-16 now," he added. "They need the weapons system."
Graham's stance contradicts the prevailing opinion among Republicans that the current administration should limit its military aid to Ukraine to avoid depleting the country's arsenal.
Interestingly, even President Joe Biden – a staunch Ukraine supporter – is not ready to commit F16s to the Ukrainians.
When asked late last month whether the White House would begin providing Ukraine with F-16s, he answered with a firm and simple "no." But the president was quick to add that he would remain in discussions with Ukraine about its weapons requests.
In a more recent statement, U.S. Ambassador to the United Nations Linda Thomas-Greenfield noted that the decision regarding sending fighter jets to Ukraine is still being negotiated.
"We have to ensure, and I think [Secretary of State Antony Blinken] said this as well, that they have the training necessary and the capacity to use weapons systems that we provide to them," said Greenfield. "Discussions will continue over the course of the next few weeks and months, as we determine how best to support them."
Last September, Graham introduced a bill along with Democratic Sen. Richard Blumenthal of Connecticut to designate Russia as a state sponsor of terrorism. If this bill had passed during that session, it would have made Russia the fifth country currently placed under that designation, after Syria, Iran, North Korea and Cuba.
With the designation, Russia's sovereign immunity before U.S. courts would be eliminated and the country would see significant reductions in foreign assistance and exports from the United States.
Biden himself has stated that he does not want to designate Russia as a state sponsor of terrorism, saying that such a move could hamper diplomatic efforts to end the conflict between the two countries.
White House Press Secretary Karine Jean-Pierre added during a press briefing that the designation would not be the "most effective or strongest path forward" to holding Russia "accountable." But the Biden administration is interested in labeling Russia as an "aggressor state."
"We're working with Congress right now on legislation that would help us get around some of the challenges of using the state sponsor of terrorism designation, which … has some unintended consequences," said Secretary of State Antony Blinken.
Watch this clip from the "War Room: Battleground" as host Steve Bannon talks to Boris Epshteyn about how the administration of President Joe Biden is blindly throwing away money and weapons for Ukraine.