Graham, a veteran foreign policy hawk representing South Carolina, was speaking to reporters after being briefed along with dozens of other senators on Venezuela strategy by Secretary of State Marco Rubio and Defense Secretary Pete Hegseth.
"If, after all this Maduro is still in power. That's the worst possible signal you could send to Russia, China, Iran," said Graham, "I want to reassert again, you cannot allow this man to be standing after this display of force."
The United States has ramped up a military deployment in the Caribbean as part of a pressure campaign on Venezuela and its leader Nicolas Maduro. US attacks on alleged drug boats there and in the Pacific have killed at least 87 people, in strikes which Democratic opponents and rights groups say violate the laws of war.
The Trump administration has branded Maduro a narco-terrorist and said drug flows from Venezuela kill innocent Americans and justify a wartime approach.
Trump has vowed to extend US attacks to the mainland and said in an interview last week that Maduro's "days are numbered," without elaborating.
His influential chief of staff Susie Wiles told Vanity Fair in an interview published on Tuesday that "(Trump) wants to keep on blowing boats up until Maduro cries uncle."
"I want clarity right here," Graham added in his remarks to reporters. "I want us to be level with the American people on what we're doing. I think we're doing a good thing. I think we're making us safer as a nation. We're cleaning up our backyard."
"Too many Americans have died ... he's aligned with Hezbollah. There's a million reasons you want Maduro to go, but just say it. Just say, this man in our backyard runs a narco-terrorist state along with international terrorists."
US Secretary of State Marco Rubio last week cast Venezuela as a regional platform for Iranian influence, describing Maduro’s government as a narcotics transit hub that hosts Iran’s Revolutionary Guards and its Lebanese ally Hezbollah.
Little public evidence exists about the security relationship Venezuela has with Iran or its armed allies. Tehran and Caracas boosted ties under Maduro's predecessor Hugo Chavez, who cast himself as a bulwark against what he called American imperialism.
Maduro has rejected US accusations that he runs a drug cartel and calls the military buildup in the region a bid to impose Washington's will on his oil-rich country.
Trump has presented himself as a peacemaker, as a leader who is ending wars as he puts it through a so-called peace through strength strategy.
The Trump administration's new National Security Strategy (NSS), released earlier this month, makes an argument for a hands-off approach to the Middle East, while showing clear willingness to lean into tensions with Venezuela.
While the Trump administration maintains their main efforts are about combatting alleged drug smuggling, Graham sees US posturing as signaling regime change, demanding clarity.
"I want clarity right here, President Trump is saying his days are numbered. That seems to me that he's got to go," Graham said.