Kennedy was "recuperating well from yesterday's procedure," his office said in a statement issued to The Associated Press. "He is experiencing no complications and has been walking the hallways, spending time with family and actively keeping up with the news of the day.
"He looks forward to returning home to Cape Cod soon, and is thankful for all the prayers and well wishes."
The 76-year-old senator is expected to stay at Duke University Medical Center in Durham for about a week before returning home to Massachusetts for further treatment. No further updates on Kennedy's condition were expected until Kennedy leaves the hospital, according to the statement.
CBS News correspondent Jeff Glor reports from Durham that Kennedy came to Duke because the medical center is known for their aggressive work in neuroscience.
"Sixty-six percent of the patients here, the brain cancer patients, undergo clinical trials," Glor said.
Kennedy was diagnosed with a malignant glioma in the left parietal lobe of his brain after suffering a seizure on May 17 at his home in Hyannis Port, Mass. He underwent 3½ hours of surgery on Monday at Duke. Doctors provided few details about the surgery, including how much of the tumor was removed.
But Kennedy's doctor said the procedure "accomplished our goals." When Kennedy emerged, a family spokeswoman said he told his wife, Vicki, that he felt "like a million bucks."
In the following days, Kennedy will probably be given drugs to prevent brain swelling and seizures, which are possible complications of the surgery. The senator also will be closely watched for bleeding and blood clots. Strokes are also a risk, but are uncommon.
"After a brief recuperation, he will begin targeted radiation at Massachusetts General Hospital and chemotherapy treatment," his doctor, Dr. Allan Friedman, said in a statement following Monday's procedure. "I hope that everyone will join us in praying for Sen. Kennedy to have an uneventful and robust recovery."
The sole surviving son of America's most glamorous and tragic political family was diagnosed last month with a malignant glioma, an often lethal type of brain tumor discovered in about 9,000 Americans a year.
Details about Kennedy's exact type of tumor have not been disclosed, but some cancer specialists have said it likely is a glioblastoma multiforme - an especially deadly and tough-to-remove type - because other kinds are more common in younger people.
Cutting a tumor down to size - or "debulking" it - is extremely delicate because of the risk of harming healthy brain tissue that governs movement and speech. But Friedman, who is the top neurosurgeon at Duke and an internationally known tumor surgeon, said Kennedy should not experience any permanent neurological effects.
CBS News medical correspondent Dr. Emily Senay explained that doctors are able to map out the parts of the brain while the patient is awake in order to protect vital functions.
"They will remove the bad part; they will do everything they can to conserve the healthy tissue so that you don't damage the person neurologically," Senay said on CBS' The Early Show. "The last thing you want to do is make the patient somehow worse off neurologically, trying to do something that in most cases is not curative."
The outlook for patients with malignant gliomas is poor, and depends on what type of glioma a patient has. Median survival for glioblastomas is 12 to 15 months, but the range is wide, said Dr. Mark Gilbert, a brain tumor expert at the University of Texas M.D. Anderson Cancer Center in Houston.
Doctors have not revealed Kennedy's treatment plan, but typical radiation treatment is five days a week for a month, using 3D imaging techniques that narrowly deliver the beams to the tumor, affecting as little surrounding tissue as possible.
Kennedy also likely will receive the chemotherapy drug Temodar during and after radiation. It can cause typical chemo side effects
nausea, vomiting and fatigue - but treatments are much better for these than even a few years ago, doctors stressed.
He also may be treated with Avastin, a newer targeted drug to deprive the tumor of its blood supply, though this is still experimental as initial treatment, rather than after patients have relapsed.