"The King has been overwhelmed with the outpouring of aroha and support," Mr Morgan said.
He is expected to be in hospital for at least a week for specialists to run a series of tests.
Mr Morgan said the King had been speaking with advisers but would not be receiving visitors at the hospital.
"He intends to return to official duties as soon as he is able," Mr Morgan said.
Mr Morgan said numerous leaders and ambassadors had extended their well-wishes to the King, for which he was grateful.
In one of his rare speaking appearances, a visibly-frail looking King Tuheitia last week addressed his health issues at his koroneihana (coronation) celebrations held at Turangawaewae marae in Ngaruwahia.
"You are well aware of my personal fight with diabetes and cancer and I am pleased to report that these are being kept under control," he said at the time.
The Herald understands he underwent a gastric bypass last year after his doctors recommended he undertake the procedure.
It's understood that the King's family have maintained their vigil at his bedside.
Both they and the Kingitanga have asked for privacy.