Clinton said she didn't understand why, given this history, some Democrats were calling for her to quit.
Her remark about an assassination during a primary campaign drew a quick response from aides to Democratic presidential front-runner Barack Obama.
"Senator Clinton's statement before the Argus Leader editorial board was unfortunate and has no place in this campaign," said Obama spokesman Bill Burton.
Clinton spokesman Mo Elleithee said the senator was only referring to her husband and Kennedy "as historical examples of the nominating process going well into the summer and any reading into it beyond that would be inaccurate and outrageous."
She has said much the same thing before. In a March interview with Time magazine, she said: "Primary contests used to last a lot longer. We all remember the great tragedy of Bobby Kennedy being assassinated in June in L.A. My husband didn't wrap up the nomination in 1992 until June, also in California. Having a primary contest go through June is nothing particularly unusual."
Within a couple hours of the South Dakota remarks drawing attention, Clinton decided to make a personal apology.
"I was discussing the Democratic primary history and in the course of that discussion mentioned the campaigns of both my husband and Senator (Robert) Kennedy waged in California in June in 1992 and 1968 and I was referencing those to make the point that we have had nomination primary contests that go into June. That's a historic fact," she said.
"The Kennedys have been much on my mind the last days because of Senator Kennedy," she added, referring to Sen. Edward M. Kennedy's recent diagnosis of a brain tumor. "I regret that if my referencing that moment of trauma for our entire nation and in particular the Kennedy family was in any way offensive. I certainly had no intention of that whatsoever.
"My view is that we have to look to the past to our leaders who have inspired us, give us a lot to live up to, and I'm honored to hold Senator Kennedy's seat in the United States Senate from the state of New York and have the highest regard for the Kennedy family," she said.
A close Obama ally in the Senate, Sen. Dick Durbin of Illinois, said he accepted her explanation.
"I know Hillary Clinton, and the last thing in the world she'd ever want is to wish misfortune on anybody. She and Barack are friends," Durbin said. "It was ... a careless remark and we'll leave it at that."
In the same editorial board meeting, Clinton said "it is unprecedented in history" for political activists to urge a candidate to withdraw when his or her chances of winning the nomination appear remote. In fact, such events have happened several times.
Three months ago, Republican hopeful Mike Huckabee angered Sen. John McCain by lingering in the GOP race after McCain's nomination seemed all but assured. "Of course I would like for him to withdraw today," McCain said at the time. A McCain campaign memo, which was leaked to the media, said the campaign was being forced to spend money in upcoming primary states merely to avoid being embarrassed by the underfunded Huckabee.
Clinton also said her campaign has had no discussions with Obama's aides about her possibly becoming his vice presidential pick.
"It is flatly untrue and it is not anything I'm entertaining. It is nothing I have planned and it is nothing I am prepared to engage in. I am still vigorously campaigning."
The Obama campaign also dismissed reports that there were talks going on between the two campaigns about putting Clinton on the ticket.
Obama has an almost 200-delegate lead over Clinton and is just 56 delegates short of the number needed to clinch the nomination, making Clinton's goal of catching him more difficult by the day. The primaries end June 3.
Clinton spent the day campaigning in South Dakota, which holds one of two June 3 primaries. At stake are 15 delegates.