The Serie A club had announced the former Marseille manager's appointment on Wednesday, with the Argentinian due to succeed Stefano Pioli on Saturday.
But the club announced on Friday there had been an abrupt about turn by the former Argentina and Chile manager, with former player Simone Inzaghi once again taking charge in a caretaker role.
A statement on Lazio's official website read: " We note with surprise the resignation of Mr Marcelo Bielsa, in clear violation of the commitments undertaken with the contracts signed last week and deposited with the League and the FIGC under their required procedures.
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" The company reserves all actions to protect its rights. It entrusts the management of the team in the final preparatory retreat to Mr Simone Inzaghi."
Lazio had only confirmed the appointment of 60-year-old Bielsa on Wednesday in his first role since resigning as manager of Marseille in August 2015.
Lazio sacked Pioli in April and named their former striker Inzaghi as boss until the end of the season.
The 40-year-old guided the club to eighth place in Serie A but their failure to win a place in the Europa League next season resulted in a move for the experienced Bielsa.
Reports on Wednesday claimed Bielsa could be named as Gerardo Martino's replacement as Argentina coach - a position the former Athletic Bilbao boss held between 1998 and 2004.
Lazio released a statement on their official website on Wednesday which read: ''As revealed by the news media, Lazio announces that it has already deposited the contract of Marcelo Bielsa and his staff.
''The club also announces that, as per the communication received, the coach and his staff will be in Rome on Saturday, July 9.''
But with Lazio announcing on Friday Bielsa had resigned, that has left the way open for him to potentially return to manage Argentina following the resignation of Martino in the wake of a second successive Copa America defeat to Chile.
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