The delay in filing the audit reports would attract disciplinary action, BSE said in a circular.
The exchange said it will charge Rs 100 per day for non-submission of system audit report for the month of December and will withdraw trading facility from January.
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Algorithmic or algo trading refers to orders on bourses that are generated using high-frequency and automated execution logic.
"The type III Brokers (those who use algo trading facility) are required to submit the system audit report for the period April 1, 2017, to September 30, 2017," it said.
The system audit report and related documents have to be filed only in electronic form through BSEs electronic filing system.
According to BSE, an auditor may perform a maximum of three successive audits for the stockbroker. The follow-on audits conducted by the same auditor, however, would not be considered as successive audits.
BSE said the count will commence from the audits conducted for the period ended March 31, 2014.
It said further that the audits should be conducted by auditors having a minimum experience of three years in information technology audit of securities market participants - stock exchanges, clearing corporations, depositories, stock brokers and depository participants.
Besides, it said, auditors should not have any conflict of interest in conducting fair, objective and independent audits of stockbrokers.
Further, the directors and partners of the auditor firm should not be related to any stock broker including its directors or promoters either directly or indirectly.
Separately, the exchange has asked trading as well as clearing members to submit the internal audit report for the first half of the current fiscal by the end of this month.