11 November 2010 Last updated at 16:38 
Gareth Compton said it was an "ill-conceived attempt at humour"
Police said he had been arrested under the Communications Act 2003 and bailed. He has since apologised.
Ms Alibhai-Brown said she found his attitude "loathsome" and that a "flippant apology" was not enough.
She had appeared on Radio 5 Live's breakfast show on Wednesday discussing human rights in China.
Afterwards, Mr Compton allegedly tweeted: "Can someone please stone Yasmin Alibhai-Brown to death? I shan't tell Amnesty if you don't. It would be a blessing, really."
Later, he wrote on Twitter that he had not called for the stoning of anybody.
He said: "I made an ill-conceived attempt at humour in response to Yasmin Alibhai-Brown on Radio 5. I [apologise] for any offence caused, it was wholly unintentional."
The Conservative Party has said his membership has been suspended indefinitely pending further investigation.
Ms Alibhai-Brown said she had been upset that somebody felt it "was OK" to say such things.
She said she had not known until the early hours, when she received a call, that anything had been written about her.
"My daughter had seen it earlier and not told me so I realised why she had been upset before she went to bed," she said.
"If I, as a Muslim woman, had said about him what he said about me then I would be arrested in these times of the war against terror," she said.
"He does not have more of a right to say these things about me that I do about him and I think words matter when you are in public life."
Roger McKenzie, Unison's West Midlands regional secretary, said he had been inundated with complaints from city council workers outraged at Mr Compton's comments and he called on Mr Compton to resign from the council.
He said: "Birmingham is a multicultural city and the council's workforce reflect this.
"It is clear that Councillor Compton is out-of-touch with both his city and the council staff.
"It is wholly unacceptable for a public official to make such racist comments. Councillor Compton must resign his seat immediately."
A Birmingham City Council spokesman said: "Any complaints that are formally received about the conduct of a city councillor are considered by the Standards Committee to determine if there is any case to answer."
The Leader of the Commons, Sir George Young, told MPs the comments were unacceptable.
"Stoning to death is a barbarous form of punishment which the government and I am sure every honourable member of this house deplores, and I hope that no elected person will threaten any member of our society with that sort of punishment," he said.
Gareth Compton said it was an "ill-conceived attempt at humour" A Conservative Birmingham City councillor has been arrested over allegations he called on Twitter for a female writer to be stoned to death.
Erdington councillor Gareth Compton made the remark about Yasmin Alibhai-Brown on his Twitter page.Police said he had been arrested under the Communications Act 2003 and bailed. He has since apologised.
Ms Alibhai-Brown said she found his attitude "loathsome" and that a "flippant apology" was not enough.
She had appeared on Radio 5 Live's breakfast show on Wednesday discussing human rights in China.
Afterwards, Mr Compton allegedly tweeted: "Can someone please stone Yasmin Alibhai-Brown to death? I shan't tell Amnesty if you don't. It would be a blessing, really."
Later, he wrote on Twitter that he had not called for the stoning of anybody.
He said: "I made an ill-conceived attempt at humour in response to Yasmin Alibhai-Brown on Radio 5. I [apologise] for any offence caused, it was wholly unintentional."
The Conservative Party has said his membership has been suspended indefinitely pending further investigation.
Ms Alibhai-Brown said she had been upset that somebody felt it "was OK" to say such things.
She said she had not known until the early hours, when she received a call, that anything had been written about her.
"My daughter had seen it earlier and not told me so I realised why she had been upset before she went to bed," she said.
Yasmin Alibhai-Brown: "Do you think stoning women is ever a joke?"
"He does not have more of a right to say these things about me that I do about him and I think words matter when you are in public life."
Roger McKenzie, Unison's West Midlands regional secretary, said he had been inundated with complaints from city council workers outraged at Mr Compton's comments and he called on Mr Compton to resign from the council.
He said: "Birmingham is a multicultural city and the council's workforce reflect this.
"It is clear that Councillor Compton is out-of-touch with both his city and the council staff.
"It is wholly unacceptable for a public official to make such racist comments. Councillor Compton must resign his seat immediately."
A Birmingham City Council spokesman said: "Any complaints that are formally received about the conduct of a city councillor are considered by the Standards Committee to determine if there is any case to answer."
The Leader of the Commons, Sir George Young, told MPs the comments were unacceptable.
"Stoning to death is a barbarous form of punishment which the government and I am sure every honourable member of this house deplores, and I hope that no elected person will threaten any member of our society with that sort of punishment," he said.
