Mr Waite joined relatives of the captives in broadcasting messages of love and support to the four men, including the Britons Keith Mangan and Paul Wells, whose whereabouts remain unknown.
Speaking on the BBC World Service yesterday, Mr Waite, formerly the Archbishop of Canterbury's special envoy, said nothing could be gained by keeping the men.
"Get rid of the problem and let the men go," he said in an interview with a fellow former Beirut hostage, John McCarthy, who now presents the programme Outlook, which sustained the two men through their own captivity.
"I am convinced that there are enough people in the world, including myself, who are prepared to take a fresh look at the problems facing people in that region but no one can do anything while hostages are still held."
Mr Mangan, 34, an electrician, from Eston, near Middlesbrough, his wife, Julie, Mr Wells, 25, a photography student from Blackburn, Lancashire, and his girlfriend, Catherine Moseley, were seized at gunpoint about 60 miles east of the Kashmiri capital, Srinigar, last year.
Mrs Mangan and Miss Moseley were later released, but the British men were detained along with an American, Donald Shelley, a German, Dirk Hasert, and a Norwegian, Hans Ostroe, by the previously unknown Al-Faran separatist group.
It demanded the release of Kashmiri militants from Indian jails and threatened to kill hostages unless their demands were met. They were not.
On 13 August last year, Mr Ostroe was found beheaded with "Al-Faran" carved on his body. His despair was marked in a note found hidden in his underwear: "I'm dying. There's nothing to eat. There's nothing to live for."
News of the remaining hostages has remained scant, with the British High Commission in Delhi working on the basis that "the hostages are very much alive" although a captured militant said they were killed on 13 December last year.
Julie Mangan yesterday recalled how she did not even have a chance to say goodbye when she was released. "He couldn't find his coat. I bent down to give him mine and when I looked up he was walking away."
In a message she hoped her husband might hear, she said: "I know that we are in each other's hearts and to say I love you is inadequate.
"I know, Keith, that you are willing me to stay strong and you must do the same."
Sarah Wells, the sister of the hostage Paul, said: "He'll be finding it hard but he'll cope because he's a strong person."
However, the health of the hostages is expected to be poor because of the cold, poor diet, unhygienic conditions and the mental strain of the ordeal. A Foreign Office spokesman said as much as possible was being done although there has been no direct contact with Al-Faran since last year.
"There have been a lot of unconfirmed sightings and some reports to the effect that the hostages are dead.
"But we are still working on the assumption they're alive. We have a lot of experts there on the ground."
Terry Waite and John McCarthy both heard messages from friends and family similar to those broadcast yesterday when they were held hostage in Lebanon.
Today is also the 30th anniversary of the Outlook programme. It can be heard in the Kashmir region.Reuse content