Britain's The Guardian newspaper reported that Lady Tonge told the party leadership that she could not accept the ultimatum from the deputy prime minister because she stood by her remarks.
Her move, which came as the Board of Deputies of British Jews condemned Tonge's remarks as "sinister and abhorrent," means she no longer holds the post of Liberal Democrat whip in Britain's House of Lords.
In her statement she said: "The comments I made were in protest at the treatment of Palestinians in Gaza and the West Bank and the treatment of Israeli Arabs."
She added: "I have been asked to apologize but refuse to do so and resign the whip of my party."
Enough is enough?
Clegg said in response: "These remarks were wrong and offensive and do not reflect the values of the Liberal Democrats.
"I asked Baroness Tonge to withdraw her remarks and apologize for the offence she has caused. She has refused to do so and will now be leaving the party."
Tonge, who was fired from a party post in 2004 when she suggested she could consider becoming a suicide bomber, sparked the row after raising questions about the future of Israel.
She told a meeting at Middlesex University last week: "Beware Israel. Israel is not going to be there forever in its present form. One day, the United States of America will get sick of giving 70 billion pounds
She added: "Israel will lose support and then they will reap what they have sown."
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