In a remarkable disclosure of private conversations, Mr Carr said he chose to publish the text messages in his book – Diary of a Foreign Minister – without getting Ms Gillard's permission, because to do so was in the national interest.
He also describes Israel's former ambassador as "cunning" and reveals his fights with the self-described pro-Israel "falafel faction" in Labor's caucus that includes Jewish MPs Mark Dreyfus and Michael Danby.
Happier times ... Prime Minister Julia Gillard with Foreign Minister Bob Carr at a press conference in Beijing China on 9 April, 2013. Photo: Andrew Meares
Mr Danby has hit back at Mr Carr, accusing him of bigotry over his claims of the influence of a pro-Israel lobby.
"No lobby in Australia, I understand, has that kind of influence. It's laughable," he told ABC radio on Thursday.
"But I suppose, in the current climate, as [Attorney-General] George Brandis says, it's OK to be a bigot."
The Jewish MP, who is chairman of the Friends of Israel, also accused Mr Carr, a former premier of NSW, of showing ingratitude to the Labor Party.
"In retrospect, given all the division he caused ... it was a mistake," Mr Danby told ABC Radio on Thursday.
"Here's a bloke plucked from obscurity ... a former provincial premier who dumps on Gillard and the former Labor government ... the Labor Party supported him all his political life. How about a bit of decency?"
Mr Danby also likened Mr Carr to Jack Nicholson's character in the film As Good as it Gets.
"A lot of people are laughing at the book; they're not laughing with you Bob, they're laughing at you," Mr Danby said.
On Thursday, Mr Carr said Mr Danby's comments were "extraordinary".
"For years I was president of Labor Friends of Israel. I wrote a book, My Reading Life, in which I recommend the book of an Auschwitz survivor as the most important book of the last 100 years," he told ABC radio.
"My only point about Israel was that settlement activity ought to stop and that the Palestinian status, the increased status in the General Assembly, ought to be not blocked by Australia. So that's a position that the foreign minister of every European country would endorse and indeed doesn't fall too much short of the foreign policy position of [US Secretary of State] John Kerry."
During his 18 months as foreign minister, Mr Carr orchestrated a significant shift in the Australian government's Middle East policy, swinging support behind Palestine at the United Nations. Standing up to Ms Gillard, who was staunchly pro-Israel, Mr Carr succeeded in forcing her to abandon her determination to oppose Palestine's attempts to gain observer status at the UN. Ms Gillard's leadership wobbled in the process.
Mr Carr's pro-Palestinian advocacy alienated many in Australia's Jewish community, and some within his own party; and the publishing of his personal diaries is likely to inflame both the Australian Israel lobby and senior Israeli officials.
Mr Carr's criticisms of Israel touch the highest levels of the Israeli government. Mr Carr describes Foreign Minister Avigdor Lieberman as "gloomy, taciturn", and the former Israeli ambassador Yuval Rotem as "the cunning Yuval".
In diary entries Mr Carr reveals just how deep his division with Ms Gillard went. He complains that Ms Gillard would not even let him criticise Israeli West Bank settlements due to her fear it would anger Australia's pro-Israel lobby – a reference to the Melbourne-based Australia/Israel & Jewish Affairs Council – which Mr Carr says had a direct line into the prime minister's office.
"So, we can't even 'express concern' without complaint," Mr Carr writes. "This lobby must fight every inch."
Reproducing private text messages, Mr Carr suggests Ms Gillard's support of Israel was so immovable that she would not even allow him to change Australia's vote on what he considered to be a minor UN motion.
"Julia – motion on Lebanon oil spill raises no Palestinian or Israel security issues. In that context I gave my commitment to Lebanon," Mr Carr writes in a text message.
"No reason has been given to me to change," Ms Gillard reportedly replies.
"Julia – not so simple," Mr Carr responds. "I as Foreign Minister gave my word. I was entitled to because it had nothing to do with Palestinian status or security of Israel."
Ms Gillard shuts him down in a final terse message: "Bob … my jurisdiction on UN resolutions isn't confined to ones on Palestine and Israel."