(CNN) Republican Sen. John Kennedy said he's done talking about Ukraine, days after stirring up a controversy with his on-again, off-again, on-again theories about whether Ukraine meddled in the 2016 US election.

"There's nothing else I'm going to say on it," he told a group of reporters who rushed to speak to him as he made his way through a crowded Capitol basement to take an elevator to the Senate floor for a vote.

CNN asked the Louisiana senator -- who is famous for his loquacious, Southern-accented and folksy manner -- if that meant he's never again talking about the Ukraine interference matter, after making headlines on the issue for days.

"No," he said, he wasn't. "Reasonable people can disagree. I believe what I believe and some people believe otherwise and they are entitled to it."

Kennedy then implored an elevator operator to help him escape the reporters and seemed to acknowledge that his shifting Ukraine views -- disputed by many other GOP senators but backed by President Donald Trump -- had hurt him.

"Ma'am, can you help me here," Kennedy called out. "These people are trying to kill me and hurt me the entire time that I'm dying."

As he finally climbed aboard the "Senators Only" elevator, he bumped directly into Sen. Mitt Romney, a Republican from Utah, who moments earlier had told many of the same reporters that he strongly disagrees with Kennedy that Ukraine interfered in the US elections.

Reporters had pressed Romney to directly criticize his fellow Republican but he declined to take their offer.

A reporter asked the senators if they were going to hash out their differences while riding up.

"Mitt said I don't have to answer," Kennedy replied as the doors shut.

Kennedy's comments Tuesday afternoon followed remarks he had made in the morning to CNN's Suzanne Malveaux after he was repeatedly asked about the evidence for his claim of Ukraine's election meddling.

"There's no question in my mind Ukraine did try to influence the election," Kennedy said Tuesday morning.

"I do believe that Ukraine tried to influence our election in 2016 and I think our media has documented it well," he said, pointing to examples including reports in the Financial Times and Politico, as well as an op-ed by the Ukrainian ambassador in The Hill, as well as Facebook posts. "Now, that doesn't mean that Russia didn't. Russia did. Russia was the master at it."

When asked if he was spreading Russian propaganda that Ukraine was involved in US election meddling, Kennedy replied, "Well, I have no way of knowing what Vladimir Putin says or thinks. I think he's a thug or a monster, but I don't think any of these periodicals have withdrawn the articles."

Moments after Kennedy and Romney exited on the elevator Tuesday afternoon, two other GOP lawmakers who are wary of the claims about Ukraine arrived. Standing in the same hallway, they told reporters that Russia is the real problem, putting on full display the GOP divide on the issue.

Trump ally Sen. Lindsey Graham -- in a notable break from the President -- sharply disputed Trump and other Republicans pushing the Ukraine theory.

"That is not true," Graham said. "They didn't. It was the Russians. I'm 1,000% confident that the hack of the DNC was by Russian operatives, no one else."

The South Carolina Republican said he has seen media reports of a possible connection between Ukraine and the hacked Democratic National Committee emails but added, "No one from the intelligence community has ever told me that happened."

Republican Sen. Mike Braun of Indiana said the US would be making a mistake if it shifted its attention to Ukraine when Russia was responsible for the election interference.

"I think Sen. Kennedy is firm in his belief that they had some impact. To me, don't take your eye off Russia. That's where I think we need to focus," he said. "They clearly have the capability and intent and will be there in some way every election down the road to the extent that they can penetrate the system."

Some GOP senators -- including several up for reelection in states where Trump is popular -- were noncommittal, leaving themselves room to support the President's theories.

Sen. John Cornyn, a Republican from Texas who is on the Intelligence Committee, told CNN on Monday that he's inclined to believe Ukraine might have been involved.

"I believe there was some open-source reporting to the effect there were actors in Ukraine actively encouraging the Clinton campaign," he said, referring to news reports. "There is a lot of intrigue that happens behind the curtains. I guess I would not be surprised if that were true."

Sen. Joni Ernst, a Republican from Iowa, said, "I would tend to believe that Russia would do something like that."

But pressed on whether the Ukrainians hadn't interfered, she wouldn't declare one way or another.

"We have not been briefed on that so I would have no way of knowing that, yes or no," she said.

At a news conference, Senate Majority Leader Mitch McConnell was questioned about the divide in his party and asked "to set the record straight."

McConnell, the longest-serving Republican Senate majority leader in history, has a well-earned reputation for saying exactly what he wants and not a drop more. Up for reelection in red Kentucky, he also knows how to avoid saying anything critical of certain subjects that are important to the President, like whether or not Ukraine interfered.

At first McConnell seemed to answer an unrelated question about the impeachment inquiry in the House before eventually being steered back by a second reporter to the original question, though McConnell still masterfully avoided providing clarity on his views about Ukraine.

"That is something for the Intelligence Committee to look at, if they choose to. And I don't have any particular reaction to it," he said.

As Sen. John Thune of South Dakota, who is second-ranking to McConnell in GOP leadership, left that same news conference, he was asked why his party was divided on the issue.

While he didn't answer that part of the question, he made clear he believes Ukraine was not involved.

"All I know is that the intelligence community and the Intelligence Committee here has concluded conclusively that it was the Russians," he said. "So, that's what I know and believe to be true. I have not seen any evidence that it was anybody else."

Senate Minority Leader Chuck Schumer said he knows why Republican are split: "Obeisance to Trump."

"This was a right-wing conspiracy theory and we're in a new time here," the New York Democrat said. "I'm just aghast that my Republican colleagues, you know, in obeisance to Trump, we know will say anything, whether it's true or not, just embrace it. It's appalling and it's shameful on them."