Sir David, they said, had "properly apologised for mistakes made at the time by the regional health authority".
Sir David Nicholson has the focus of anger from families affected by the scandal.
The British Medical Association's letter to Sir David Nicholson follows reported problems in trial areas.
Shadow health secretary Andy Burnham has said NHS boss Sir David Nicholson should remain in post.
She is adamant Sir David, who has apologised for what happened, should lose his job.
Sir David said it was "perfectly understandable" that some were calling for his resignation.
Renishaw founder and Chief Executive Sir David McMurtry told BBC News he remained optimistic.
Sir David Steel and George Reid brought long experience and clear minds to the task.
During a meeting of the board chairman Prof Malcolm Grant publicly backed Sir David.
Trust interim chairman Sir David Henshaw said it would be replying to the minister later.
But even if Sir David's proposals are enacted, will the legal profession become much more consumer-oriented?
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On Monday, Sir David Varney rejected demands for a cut in corporation tax in NI.
Rangers began using the EBT scheme while under the control of Sir David Murray.
Sir David's comments came in an Oxford University lecture reported in the Daily Telegraph.
Mr Salmond welcomed the report and thanked Sir David for his "very thorough and detailed" work.
But Scottish Conservative leader Ruth Davidson said Sir David's inquiry was a "sham process".
"Saddam Hussein has had years in which to co-operate, " Mr Hoon told Sir David Frost.
Of course, this will be influenced by ministers as well as senior officials such as Sir David.
About a dozen people held placards calling for the resignation of NHS Chief Executive Sir David Nicholson.
Finance Minister Peter Robinson also expressed his extreme disappointment at the outcome of Sir David Varney's review.
New chair Sir David Henshaw said the trust was now at "the beginning of a new start".
More than half of women prisoners, according to Sir David's report, have severe emotional or psychological problems.
There have been calls for Sir David's resignation over the failings, which led to hundreds of needless deaths.
Sir David's inquiry concentrated on the supervision he received from Cheshire probation service, on his release in 2001.
Sark's government has been involved in a court battle with Brecqhou residents Sir David and Sir Frederick Barclay.
By complaining in his loud, military voice, Sir David has caused some improvements and a lot of embarrassment.
Sir David Henshaw, Chair, UHMBT said he was "extremely disappointed" with the decision which he called "fatally flawed".
In repeated reports, Sir David has drawn attention to the good practice he has seen during his inspections.
Sir David Barclay and his brother Sir Frederick also own the Daily Telegraph and the Littlewoods retail group.
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Head of the British army, Gen Sir David Richards, said the milestone death had hardened "our determination to succeed".
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