"I deeply regret my friendship with Jeffrey Epstein. It is important for me to apologise to all of those whom I have disappointed ... I also regret the situation I have put the royal family in, especially the king and queen," she said in a statement from the palace.

Some said Warsh, who believes the central bank needs to change the way it has operated over recent decades, is the right man for the job. Others doubted if he would just be a "yes man" for the president.