"Take care of my friend," the Republican leader told Kennedy's wife, Vicki, who answered the call at Massachusetts General Hospital, according to a family spokeswoman.
While Kennedy remains a conservative target, Mr. Bush has hosted him socially at the White House and worked with him to pass a signature administration achievement, the No Child Left Behind education law.
"The senator and Mrs. Kennedy were very appreciative of the call," spokeswoman Stephanie Cutter said. Over the weekend, Kennedy fielded similar calls from Sens. Barack Obama of Illinois and Charles Schumer of New York, while receiving visits from Sen. John Kerry of Massachusetts, other dignitaries and a stream of family members.
The liberal icon was admitted to Massachusetts General on Saturday after becoming ill after walking his dogs at his oceanfront home on Cape Cod. Despite suffering what appeared to be stroke-like symptoms, the senator's primary care physician later said a stroke had been ruled out and Kennedy appeared to have been the victim of a seizure.
Dr. Larry Ronan and other physicians were conducting a battery of tests, the results of which may not be available until late Monday or Tuesday.
Kennedy, 76, underwent surgery last October on the left carotid artery in his neck after doctors discovered a near-complete blockage that left him with an elevated risk of a stroke. The senator has since resumed a hectic schedule, including campaigning for Obama and bouncing between appointments on Capitol Hill and in Massachusetts.
Cutter said the senator had a restful night at the hospital after spending Sunday watching sports and movies and visiting with family.
Bush had been notified of Kennedy's hospitalization just before he went to a Saturday night dinner meeting with Palestinian President Mahmoud Abbas during a tour of the Middle East. The president called the Kennedys from the White House, where he returned Sunday.