Councillor Collin Brewer, pictured right, independent member for Wadebridge East, made the comments to Disability Cornwall at an information event at County Hall in Truro.
When told how the group helps parents of children with special educational needs, Mr Brewer responded by saying: "Disabled children cost the council too much money and should be put down."
Disability Cornwall advice services manager Theresa Court said: "I was absolutely horrified anyone would make such a depraved comment, let alone a Cornwall councillor and at a public event. As far as I was concerned, I had a duty to make a formal complaint against Councillor Brewer to seek appropriate justice."
An investigation was launched and the independent standards committee has now ruled that Councillor Brewer should write a letter of apology to the organisation.
His letter read: "I am writing to offer my whole hearted apology for the offence these remarks have clearly caused.
"While I meant no offence by my remarks to you I can see, in retrospect, that they were ill judged and insensitive and should not have been made at all."
The charity, which is based in Hayle, had an information stand at an event in October 2011 to allow councillors to meet equalities organisations and understand some of the issues they face.
Chairman of Disability Cornwall Steve Paget added: "It is of great concern to us that anyone with such beliefs, let alone to vocalise them, could be a representative and elected member of our local authority.
"For such a serious issue and multiple breach of code of conduct, bringing the council into disrepute, we did expect no less than this councillor's resignation."
That call was backed last night by Liberal Democrat Councillor Jan Powell, whose daughter is disabled.
She said: "I'm shocked, I can't believe that a councillor could even contemplate saying something like that even to stimulate debate. For me it is a resignation issue."
Councillor Brewer, who has been a councillor for more than 25 years, said he believed the incident happened after a long council meeting regarding budgets.
He recalled the conversation happened at a time when some disabled children were being moved out of county for care which was "incurring additional expense".
While admitting using the language, he stressed it was not something he believed but did it to "stimulate" a debate.
"I said something which was offensive and I have apologised," he told the Western Morning News last night. "I never ought to have said it.
"I said it to stimulate conversation, if you will, but it was the wrong type of thing to say. It is not something I believe. I didn't get the reaction I wanted."
Speaking from his home in Sladesbridge, near Wadebridge, Mr Brewer also admitted it was "not the type of thing you want to hear from a councillor".
"We all make mistakes," Mr Brewer, a former vice-chairman of Cornwall County Council, said. "I would have apologised there and then but I didn't get the chance."
But he added: "It is not something I would consider resigning over. I believe I am doing a good job."
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