The South Carolina Republican said he is "encouraged there are plans to continue talking" with North Korea after Trump failed to secure a formal pledge of any kind during the summit with Kim in Hanoi, Vietnam, but Graham but also warned that the clock is ticking for negotiators to convince Pyongyang to peacefully surrender its entire nuclear arsenal.
"There is only one good deal: the complete denuclearization of North Korea in return for security guarantees and economic assistance," Graham tweeted.
"We must not go back to the status quo," he added. "If negotiations fail, it would be time to end the nuclear threat from North Korea -- one way or the other."
That all or nothing view has sparked backlash from some nuclear weapons experts, who believe Graham's suggestions could yield dangerous consequences if Trump chooses to follow his advice.
"Sen. Graham is clinging to a dangerous world that fortunately doesn't exist," according to Adam Mount, senior fellow and director, Defense Posture Project, Federation of American Scientists.
"In this fantasy, Trump hasn't praised and flattered a despot, sanctions pressure is dramatically more effective than it has been and the risks of a nuclear war are tolerable. We should all be very thankful that Sen. Graham is working in a fantasy world rather than the administration," he said.
Still, Graham has emerged as an influential foreign policy adviser to the President and a staunch ally of the administration on a broad swath of issues.
That said, he has also not shied away from publicly criticizing Trump over matters on which they disagree, including the President's more diplomatic rhetoric toward Kim leading up to the second summit.
"This love crap needs to stop," Graham said in October about Trump's effusive praise for the North Korean dictator.
Trump's performance in Hanoi appears to have done little to change Graham's view that the US must take a hard line on North Korea, even if that means considering the use of preventative military force should Kim refuse to peacefully dismantle his entire nuclear weapons program.
Despite repeatedly saying he hopes military options are never employed, Graham again made it very clear Thursday that he believes the US must be ready to pre-emptively use force against North Korea if necessary.
In 2017, when tensions between the US and North Korea were arguably at their highest, Graham predicted that there was a 30% chance Trump would order a first strike on North Korea to prevent the rogue nation from acquiring a nuclear weapon capable of hitting the United States.
Asked at the time whether he was referring to a pre-emptive strike, Graham said: "Sanctions will never work completely without the threat of credible military force. How do you change a man's behavior who's willing to kill his own family, torture his own people to stay in power?"
"The only way he'll change his behavior, if he believes Donald Trump would use military force to destroy his regime," he added, noting that his prediction on the chance of a war with North Korea was "based on a lot of time with President Trump."
Graham remained steadfast in his view that Trump should take a hard line on North Korea, even as tensions began to de-escalate, openly criticizing the President for his public praise of Kim as recently as late last year.
Questions about Trump's approach
Graham's harsh words did little to temper Trump's enthusiasm leading up to the summit but the President's failure to secure any formal agreement related to nuclear weapons in Hanoi has once again raised questions about the administration's diplomatic approach.
"It is the clearest indication in a year that the two sides are talking past each other. Further progress will require a fundamental reassessment of US negotiating policy," according to Mount.
While the two sides have offered differing accounts of what transpired during the summit, it seems the two countries were not even able to establish a shared definition of denuclearization, something Trump's top envoy on North Korea, Steve Biegun, said last month was a goal for negotiators.
While Biegun did not give a timeline for when that definition would be needed, he indicated at the time that it was a pivotal piece to the puzzle.
"There was no detailed definition or shared agreement of what denuclearization entails," Biegun said during a speech at Stanford University.
"So we do not have a specific and agreed definition of what final, fully verified denuclearization or comprehensive, verifiable, irreversible denuclearization -- whatever your preferred term of art -- is. We do need to have a shared understanding of what the outcome is going to be, and within the space that that creates, we should be able to also agree on the steps necessary to achieve a mutually accepted outcome."
"The US version of events would represent a considerable departure from what we know of North Korea's negotiating position to date. If in fact a permanent nuclear and missile test freeze was offered and passed by, it is a missed opportunity. An all or nothing bet on complete disarmament will leave you with nothing," Mount said.
"Unfortunately, we may never have a reliable account of the events of the summit, given the Trump administration's track record of concealing and distorting diplomatic readouts. It is a possibility that will complicate US policy toward North Korea for years to come," he added.
Despite leaving Hanoi without any concrete agreement or even a clear road map for future talks, Secretary of State Mike Pompeo said after the summit that the US negotiating team did "really good" work despite having little time to prepare.
Yet Pompeo also acknowledged that the potential for real progress was ultimately in the hands of Trump and Kim.
"You don't know which ones you are actually going to get until the two leaders actually have a chance to get together," he said. "There was a lot of preparatory work. We were prepared for the potentiality of this outcome as well. And tomorrow we will get right back at it."
Pompeo said he believes Biegun and his counterpart will get together "before too long." But nothing is set in stone.
"We'll see," said Pompeo, explaining that both sides need to regroup and there would need to be a reason to meet.
"Look, there has to be a reason for the conversations. There has to be a theory of the case about how to move forward. I'm confident that there is one," he said.
Pompeo acknowledged that the nuclear threat North Korea poses is still very real.
CNN's Kylie Atwood contributed to this report.
