But Mr Bannon wanted the “stronger on Israel” label for himself, Mr Wolff wrote, saying the Breitbart editor was set on making Mr Kushner appear weak and inadequate.
A passage in Chapter 10 of the book reads: “After months of defending Bannon against liberal media innuendo, Kushner had concluded Bannon was an antisemite. That was the bottom-line issue.
“This was a complicated and frustrating business – quite hard to communicate to his father-in-law because one of Bannon’s accusations against Kushner, the administration’s point person on the Middle East, was that he was not nearly tough enough in his defence of Israel.”
The book describes how Mr Kushner impressed his father-in-law by pushing for Gary Cohn, the former president of Goldman Sachs, to be the president's top economic adviser.
Mr Bannon had wanted CNBC’s conservative anchor and commentator Larry Kudlow to take on the role.
The two continued to clash until Mr Bannon was fired by Mr Trump in August 2017.
Mr Wolff wrote: “Bannon regarded Kushner and Cohn (and Ivanka) as occupying an alternative reality that had little bearing on the real Trump revolution.
“Kushner and Cohn saw Bannon as not just destructive but self-destructive, and they were confident he would destroy himself before he destroyed them.”