The Australian Securities and Investments Commission filed civil proceedings in the Federal Court on Tuesday.
The statements in question relate to a replacement plan for the computer systems used to record shareholdings and manage the settlement of share transactions, according to ASIC.
It alleges statements made in ASX announcements on February 10, 2022, that the project remained "on-track for go-live" in April 2023 and was "progressing well" were misleading.
Those representations were misleading and deceptive because, at the time of the announcements, the project was not tracking to plan and ASX did not have any reasonable basis to imply it would meet future milestones, according to ASIC.
The scheme, known as CHESS replacement project, was paused in November 2022.
Chair Joe Longo said the the statement's were a "collective failure" by the ASX board and senior executives.
"Companies and market participants rely on what the ASX says about its operations to make their own decisions and investments," he said.
"We expect the ASX to be a place to list and invest with confidence. When the ASX falls short, it has wide ranging consequences across the market."
ASX managing director and chief executive Helen Lofthouse said the organisation made "strong progress" since the statements were made.
"We recognise the significance and serious nature of these proceedings," she said.
"We co-operated fully with ASIC's investigation and are now carefully reviewing and considering the allegations."
ASX is set to report its FY24 results on Friday.
ASIC is yet to determine the penalty it will seek for ASX's alleged contraventions.
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