Former US president Donald Trump spat an expletive about his old ally, Israel's ex-prime minister Benjamin Netanyahu, for congratulating Joe Biden on his victory in last year's election, according to a new book.

Trump lashed out in an interview for a book on US-Israel relations during his presidency, author Barak Ravid wrote on the Axios website on Friday.

"Donald Trump and Benjamin Netanyahu were the closest of political allies during the four years they overlapped in office, at least in public. Not anymore," Ravid wrote.

"I haven't spoken to him since," Trump told Ravid in an interview. "F*** him."

Ravid said that he interviewed Trump twice for his forthcoming book, "Trump's Peace: The Abraham Accords and the Reshaping of the Middle East."

He said Trump, who appeared close to Netanyahu while president from 2017 to 2021, was repeatedly critical of him in the interviews.

"The final straw for Trump was when Netanyahu congratulated President-elect Biden for his election victory while Trump was still disputing the result," Ravid wrote.

Netanyahu offered his congratulations some 12 hours after Biden's victory became clear.

Trump has never conceded the election, claiming without evidence that Biden won by vote fraud.

Other foreign leaders congratulated Biden earlier than the Israeli leader, but for Trump Netanyahu stood out.

"The first person that congratulated [Biden] was Bibi Netanyahu, the man that I did more for than any other person I dealt with," Trump said, according to Ravid.

"Bibi could have stayed quiet. He has made a terrible mistake," Trump said, using Netanyahu's nickname.

"I liked Bibi. I still like Bibi. But I also like loyalty," he said.

Ravid writes that Trump was unhappy that Netanyahu did not help him remain in office.

Netanyahu responded to the Axios story in a statement Friday.

"I highly appreciate President Trump’s big contribution to Israel and its security," he said.

"I also appreciate the importance of the strong alliance between Israel and the US and therefore it was important for me to congratulate the incoming president."

Both former leaders could return to power.

Trump remains the de facto leader of the Republican Party and is keeping open the option of running for president in 2024. Netanyahu, who lost power earlier this year, is currently leader of the opposition in Israel's Knesset.