Bar's dismissal provoked the anger of the opposition and led to demonstrations accusing Netanyahu of threatening democracy.
Several thousand people braved bad weather late Thursday to demonstrate outside Netanyahu's private residence in Jerusalem and then the Israeli parliament, where ministers were meeting.
In a letter made public on Thursday, Bar said Netanyahu's arguments were "general, unsubstantiated accusations that seem to hide the motivations behind the decision to terminate (his) duties".
He wrote the real motives were based on "personal interest" and intended to "prevent investigations into the events leading up to October 7 and other serious matters" being looked at by the Shin Bet.
He referred to the "complex, wide-ranging and highly sensitive investigation" involving people close to Netanyahu who allegedly received money from Qatar, a case dubbed "Qatargate" by the media.
Bar's dismissal comes after the Israeli army launched a series of massive and deadly bombardments on the Gaza Strip on Tuesday, following a two-month truce and "targeted" ground operations.
Netanyahu said the operations were intended to put pressure on Hamas to release the 58 hostages remaining in the territory.
In rare criticism of Netanyahu, Israeli President Isaac Herzog said Thursday that he was worried the resumption of strikes in a time of crisis could undermine "national resilience".