Francis Rock repeated the claim in last week's Portadown Times, and yesterday Mayor Robert Smith said, "I believe the time has come to put the record straight that all councillors - across the board - supported Francis Rock and his family during and since the despicable threat on his life.
"We still feel that sympathy and support, and we are dismayed at his recent statements that we did not support him."
And to prove that support, Councillor Smith has released the contents of a card he received from the Rock family, "thanking me personally and the council in general for our letters and statements of support".
In his card of acknowledgement, Mr Rock said, "We have been overwhelmed by the reaction of so many people to what has happened, and we have been particularly touched by the support of my staff.
inquiries
"However, the expression of support from councillors, especially your good self (Councillor Smith) and your father (Alderman Woolsey Smith) are the most valuable of all."
Said the Mayor,"This does not reflect an uncaring council. It is regrettable that I have had to release personal correspondence, but in the light of ongoing statements that the council has been unfeeling, I believe it had to be done.
"The council would like to instigate an internal inquiry, but all inquiries have to be left to the PSNI who are better equipped and placed to get to the truth.
"Frankly, none of the councillors know who is behind this heinous threat, but we are co-opersating 100 per cent with the police and we hope and pray they get to the bottom of it."
Mr Rock has also sent an e-mail to his staff, in which he stated, "The PSNI investigation is continuing and I know I can count on everyone to give their fullest support to the police in order that those who are behind the threat are brought to justice."
And he thanked everyone who came to see him, sent messages of support, e-mails, cards, flowers and presents.
The council's website also contains his thanks for the support of staff, members and friends.
Mr Rock is quoted as thanking the then Mayor, Councillor Kenneth Twyble, for allowing him to speak publicly at a meeting following the threat.
The threat came in the form of a letter containing a bullet, and a message in block letters.
Mr Rock has been on sick leave, through stress, since November, shortly after the first anniversary of the death threat.