Khan has denied allegations of misconduct that were reported to the court's governing body last month. At that time he asked the court's own internal oversight body to investigate them.
The president of the ICC said the presiding judge in the case, Romanian magistrate Iulia Motoc, had asked to be replaced on health grounds on Friday.
Israel filed an official objection that questioned the legality of the ICC prosecutor's request to issue arrest warrants against Netanyahu and Gallant
The ICC is currently weighing a request for arrest warrants against Israeli and Hamas leaders made earlier this year.
UK Lawyers for Israel has threatened to report ICC chief prosecutor Karim Khan for professional misconduct, alleging that his accusations against Israeli leaders are false.
In court filings made public Friday, prosecutor Karim Khan urged judges weighing the arrest warrants sought against Israeli officials and Hamas leaders to not delay.
The organization tackles ICC's controversial arrest warrants, questioning jurisdiction and prosecutorial fairness in a high-stakes legal battle involving Israeli and Hamas leaders.