LONDON, SEPT. 11 -- Terry Waite, the Anglican Church envoy held hostage in Beirut for more than three years, has been ill but is alive, released Irish hostage Brian Keenan told Britain's Independent Television News in an interview Monday.

"He was in the same apartment as I was being held in," but in an adjoining room, Keenan said. Waite's cousin, John Waite, said this was the first confirmation in more than three years that Terry was alive. "It is wonderful news," he said.

The Most Rev. Robert Runcie, the archbishop of Canterbury, said today he was heartened to have "clear confirmation" Waite was alive and said there were signs of progress in efforts to free him. But he said he did not plan to go to Lebanon to try to speed any release, saying it was "not the time for gimmickry or the pursuit of tempting shortcuts."

Keenan, who was released last month after four years in captivity, said he heard the guards calling Waite by his first name. He said he is sure they were talking to Waite and not Terry Anderson because he heard Waite speak and recognized his English-accented voice from an earlier television interview.

"I know he has been ill and the illness I do not think is serious," Keenan said.

Waite disappeared Jan. 20, 1987, after leaving his Beirut hotel to negotiate with the Moslem extremist group Islamic Jihad for the release of hostages. No group has claimed to hold him, but he is widely believed held by Islamic Jihad.

Keenan said he knew Waite had been ill because "I heard him coughing very heavily at night."

"Although we didn't visually see him, we heard and I could hear under the door. His door was adjacent to mine," he said.

Keenan said his captors told him the British hostages could be free within months. "There is something happening, there is a change in the organization that is holding" the hostages, he said, without elaborating.