Spokeswoman Stephanie Cutter said he is "conscious, talking, joking with family."
His wife, children and niece Caroline Kennedy are among those with him at the hospital.
Senator Kennedy, the lone surviving son in a famed political family, was undergoing tests at Massachusetts General Hospital to determine the cause of the seizure, spokeswoman Stephanie Cutter said.
"Senator Kennedy is resting comfortably, and it is unlikely we will know anything more for the next 48 hours," she said.
Senate Majority Leader Harry Reid, speaking at the Nevada Democratic Convention in Reno, said he spoke to Kennedy's wife Saturday afternoon and was told "his condition is not life-threatening, but serious."
"But the one thing I can say, if there ever was a fighter, anyone who stood for what we as Americans, we as Democrats, stand for, it's Ted Kennedy," Reid said.
Kennedy went to Cape Cod Hospital on Saturday morning "after feeling ill at his home," Cutter said. After discussion with his doctors in Boston, Kennedy was taken to Massachusetts General.
An official who declined to be identified by name, citing the sensitivity of the events, had earlier said that Kennedy had stroke-like symptoms. The hospital declined to comment on his condition.
In October, Kennedy had surgery to repair a nearly complete blockage in a major neck artery. The discovery was made during a routine examination of a decades-old back injury.
The hourlong procedure on his left carotid artery -- a main supplier of blood to the face and brain -- was performed at Massachusetts General. This type of operation is performed on more than 180,000 people a year to prevent a stroke.
The doctor who operated on Kennedy said at the time that surgery is reserved for those with more than 70 percent blockage, and Kennedy had "a very high-grade blockage."
Distinguishing between a seizure and TIA, often called a mini-stroke, can sometimes be difficult.
Seizures are little electrical storms in the brain. They tend to be brief; an occasional one can happen to anyone even without a prior history of seizures, especially if there has been some prior brain trauma.
A stroke is either ischemic -- a clog in a blood vessel -- or hemorrhagic, bleeding in the brain. Hemorrhagic ones are very rare. Kennedy had the carotid artery surgery to try to prevent the ischemic type.
A stroke kills brain tissue; how much depends on how big it is and how long it lasts. Some people show no lasting effects; others can be partly paralyzed on one side or somewhere in-between.
Kennedy, the second-longest serving member of the Senate, was elected in 1962, filling out the term won by his brother, John F. Kennedy.
Kennedy is the lone surviving son in the famed family. His eldest brother, Joseph, was killed in a World War II airplane crash. President John Kennedy was assassinated in 1963 and his brother Robert was assassinated in 1968.
Kennedy is active for his age, maintaining an aggressive schedule on Capitol Hill and across Massachusetts.
He has been vocal in both his opposition to the Iraq war and support for Democratic presidential contender Barack Obama. He made several campaign appearances for the Illinois senator in February, and most recently another in April.
Always concerned about maintaining his health, Kennedy regularly consults with a battery of Massachusetts General doctors. It was during routine exams last year that doctors discovered the blockage in his carotid artery.
Still, he maintains homes in both Boston and Washington and attends not only official events, but numerous others recognizing his family's political history.
Just last week, he and his niece Caroline Kennedy awarded the annual "Profiles in Courage" award commemorating President Kennedy. And on Friday, he attended a ribbon cutting at the Bedford Whaling National Historical Park.
He was preparing to host the annual Best Buddies Challenge event on Saturday afternoon, a fundraiser for the Best Buddies organization founded by Anthony Kennedy Shriver that helps people with intellectual disabilities.
On Saturday, a Hyannis Fire Lt. Bill Rex said a 911 call came in from the Kennedy family compound at 8:19 a.m. A man was transported to Cape Cod Hospital and transferred by air at 10:10 a.m. from Barnstable Municipal Airport to Boston.
David Reilly, a spokesman for Cape Cod Hospital, confirmed Kennedy was brought to the hospital.
California Gov. Arnold Schwarzenegger and his wife, Maria Shriver, Kennedy's niece, said they appreciated all the messages of care they had received for the senator.
"It's always a comfort to the family to know that Sen. Kennedy is in the prayers of millions," their statement said.
Sen. John Kerry of Massachusetts, who went to the hospital, New York Sen. Hillary Rodham Clinton and Obama said were offering their prayers for his quick recovery.
Obama, beginning a tour of hospitals in Eugene, Ore., told reporters that he had been in touch with the senator's family. He said, "We are going to be rooting for him. I insist on being optimistic about how it's going to turn out."
A man walking by Massachusetts General was startled by the news when he asked about the reason for the large media presence. "Ted? Is he all right? Jeez, I'm taken aback. I just saw him on television yesterday," said Jerry Leonard, 76.
"He's a Kennedy. His name is synonymous with this area," the retired bartender said. "I'm a Bostonian, too, and he's done a lot for us around here and for the senior citizens in particular."
