Mr Graham, an ally of Donald Trump and member of the powerful senate foreign relations committee, speculated that the hermit kingdom would not let rumours of its leader’s death go unanswered for so long.
“Well, it's a closed society, I don't know anything directly,” he said. “But I'd be shocked if he's not dead or in some incapacitated state because you don't let rumours like this go forever or go unanswered in a closed society, which is really a cult, not a country, called North Korea.”
“So I pretty well believe he is dead or incapacitated,” he told Fox News.
Rumours of Kim Jong Un’s death have swirled since he missed the commemoration of the 108th birthday of his grandfather, North Korea founder Kim Il Sung, ten days ago.
North Korean authorities have said nothing to counter media reports that Mr Kim is unwell, prompting concerns about who is next in line to run a nuclear-armed country that has been ruled by the same family for seven decades.
Reuters reported this week that China has dispatched a team to North Korea including medical experts to advise on Kim Jong Un, citing three people familiar with the situation.
Adding fuel to the rumours, a train that likely belongs to the North Korean leader has been parked at his compound since last week, according to satellite imagery.
The satellite photos released by 38 North, a website specialising in North Korea studies, don't say anything about Kim's potential health problems, and they echo South Korean government intelligence that Kim is staying outside of the capital, Pyongyang.
"The train's presence does not prove the whereabouts of the North Korean leader or indicate anything about his health, but it does lend weight to reports that Kim is staying at an elite area on the country's eastern coast," it said.
South Korean and US officials have repeatedly indicated that there have been no unusual signs that could indicate health problems for Kim.
A US official, speaking on condition of anonymity because he wasn't authorised to talk to the media, told Reuters the latest rumors about Kim's health had not changed the US assessment of the information as "speculation."
White House counsellor Kellyanne Conway wouldn't comment on Kim's status. "The president will make any announcement about a head of state," she said Saturday night on Fox News Channel's ‘Justice With Judge Jeannine.’
— With agencies