(CNN) -- As he returned to the campaign trail this weekend, Republican presidential hopeful Rudy Giuliani was still facing questions about his brief hospital stay several days ago, but assured reporters he was fine.
"I've had all these tests taken the other day. They all came out 100 percent," Giuliani told CNN on Saturday.
"I'm in very good health. I had a very bad headache, that's what precipitated it, and they checked out everything."
The former New York City mayor -- who has cut back on his originally scheduled campaign events this weekend -- was admitted to a hospital in St. Louis, Missouri, on Wednesday.
Doctors put the former mayor through a battery of tests during his overnight hospital stay. His campaign has so far not revealed what conditions those tests were intended to rule out.
After hours of silence from Giuliani's campaign staff, a spokeswoman told reporters at dawn Thursday that the tests found "nothing was alarming" -- but would not elaborate on what the results were.
On Friday, Giuliani visited his personal physician. The next day, as he resumed his lighter schedule, the candidate told reporters he had simply been suffering from a massive headache worsened by insufficient cabin pressure in the small plane he was using on the campaign trail. Watch Giuliani talk about his health scare »
Giuliani had been told that "if his headache persisted he could take an aspirin for the headache pain," one campaign official told CNN.
But others said the former mayor was taking a daily dose of aspirin on a doctor's recommendation. That recommendation is standard practice for heart concerns, though both the mayor and his staff have said that his heart is fine.
"Aspirin is actually a pretty powerful drug, [though] people don't think of it that way," said CNN's chief medical correspondent, Sanjay Gupta, who added that he had not examined the mayor himself, and did not want to speculate on his condition.
"Aspirin actually causes your blood to become a little bit thinner, which is so important for someone perhaps who's a risk for having heart disease, at risk of having stroke.
"If there's been a concern about those things, the doctor may say, 'Look, you didn't have a heart attack, you didn't have a stroke, but we're concerned about it and we are going to start you on an aspirin a day,' " Gupta explained.
The Giuliani campaign insisted he has a "clean bill of health."
Giuliani said he had been given "every test imaginable," but would not reveal what those tests had been. He said his doctor would disclose more information soon.
CNN and other news organizations have asked the Giuliani campaign to release all currently available records of his recent medical treatment. The campaign has, so far, declined.
Giuliani, who was treated for prostate cancer in 2000, told CNN in April that all of his subsequent medical screenings had been negative and that "for all intents and purposes, the cancer is cured."
"I'm very healthy now," he said. "But, of course, I get tested every six months, which you're supposed to do." E-mail to a friend
CNN's Dana Bash and Mary Snow contributed to this report.
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