(CNN) -- Sen. Hillary Clinton said Sunday some people are using her controversial reference to Robert F. Kennedy's assassination to suggest that she meant something "completely unthinkable."
Sen. Hillary Clinton says her supporters urge her to stay in the race until it is over.
Her campaign also accused the rival Obama campaign of "inflaming" the situation and purposely taking her words out of context. But the Obama campaign said it was not trying to "stir the issue up."
In an editorial in the New York Daily News, the Democratic presidential hopeful also acknowledged her dwindling chances of winning the nomination, saying she is aware of "the odds" against her.
Headlined "Hillary: Why I continue to run," the editorial began with an explanation of her reference to the assassination when she was speaking to the Argus Leader newspaper in South Dakota. She said she was pointing out that presidential primary campaigns have continued into June.
"Almost immediately, some took my comments entirely out of context and interpreted them to mean something completely different -- and completely unthinkable," she wrote. Watch Hillary's camp insist the remark had nothing to do with Obama »
Clinton said the newspaper's editor and Bobby Kennedy Jr. issued statements arguing that was the meaning of her remark. No other member of the Kennedy family has issued a public statement on the matter.
"I realize that any reference to that traumatic moment for our nation can be deeply painful -- particularly for members of the Kennedy family, who have been in my heart and prayers over this past week," she said, in a reference to Sen. Edward Kennedy's diagnosis with brain cancer. "And I expressed regret right away for any pain I caused.
"But I was deeply dismayed and disturbed that my comment would be construed in a way that flies in the face of everything I stand for -- and everything I am fighting for in this election." Some people -- particularly a number of bloggers -- have suggested she was imagining the possibility that Sen. Barack Obama, the likely nominee, could be assassinated.
After Clinton's initial remarks to the newspaper were reported, the Obama campaign issued a statement saying the comment "was unfortunate and has no place in this campaign."
But Obama himself later said, "I don't think that Senator Clinton intended anything by it," and that "we should put it behind us."
Clinton campaign chairman Terry McAuliffe, in an interview Sunday, criticized the Obama campaign's first move. "It's unfortunate -- a hyped-up press over Memorial Day weekend, the Obama campaign inflaming it, tried to take these words out of context," he told "Fox News Sunday."
Asked about the remark by Obama himself, McAuliffe responded, "That's great, but Friday they were all part of this process. The press secretary came out and attacked Senator Clinton and got it going so the story would be around for three days."
Howard Wolfson, a Clinton adviser, told CBS' "Face the Nation" that the Obama campaign's first statement critical of Clinton was "unfortunate."
But Obama's chief strategist David Axelrod told ABC's "This Week" that "we take her at her word," and he added, "We're beyond that issue now, so certainly we're not trying to stir the issue up."
The program's host, George Stephanopoulos, noted that a member of Obama's staff sent to the media Saturday a "searing commentary" by MSNBC's Keith Olbermann slamming Clinton for her remark.
"Mr. Olbermann did his commentary and he had his opinion," Axelrod responded, adding, "As far as we're concerned, this issue is done."
On another front, Axelrod slammed Clinton for suggesting she leads Obama in the popular vote.
Clinton has been making that argument, based on figures that include Florida and Michigan, even though Obama took his name off the ballot in Michigan and neither candidate campaigned in Florida. The Democratic Party discounted both states' primaries before they took place.
"It would take some very tortured math and tortured logic to say that she's ahead in the popular vote," Axelrod told ABC.
He added, "This isn't 'American Idol,' OK? This is a nominating process. We have rules. We elect delegates state by state."
In her column, Clinton said she believes she can still "win on the merits."
"I am not unaware of the challenges or the odds of my securing the nomination -- but this race remains extraordinarily close, and hundreds of thousands of people in upcoming primaries are still waiting to vote," she wrote.
She added that her parents "did not raise me to be a quitter -- and too many people still come up to me at my events, grip my arm and urge me not to walk away before this contest is over."
She also said she is running "because I believe staying in this race will help unite the Democratic Party. I believe that if Senator Obama and I both make our case -- and all Democrats have the chance to make their voices heard -- in the end, everyone will be more likely to rally around the nominee."
She repeated her vow to campaign for Obama if he gets the nomination, and wrote, "No matter what happens in this primary, I am committed to unifying this party."
Obama was in Middleton, Connecticut, where he was standing in for the ailing Edward Kennedy who was scheduled to deliver the commencement at Wesleyan University. Watch Obama tell graduates they have an obligation »
The theme of Obama's speech was service, and the senator asked graduates to volunteer their time at home and abroad to fight poverty, preserve peace and protect the environment
"But I hope you'll remember, during those times of doubt and frustration, that there is nothing naive about your impulse to change this world," he said. "Because all it takes is one act of service -- one blow against injustice -- to send forth that tiny ripple of hope that Robert Kennedy spoke of."