The adultery website targeted by hackers is offering a 500,000 Canadian dollar (£240,000) reward for information about those behind the leak.
The entire Ashley Madison client list, which claims to have more than 30 million users worldwide including in the UK, was published online, triggering extortion attempts and two unconfirmed reports of suicides, Canadian police said.
The website, whose slogan is "Life is short. Have an affair", is marketed to facilitate extramarital affairs.
The group claiming to be behind the attack - The Impact Team - first breached Ashley Madison's servers last month but released the data last week to the Dark Web - a sub-level of the internet that cannot be accessed through normal browsers, and is often described as the "internet black market".
However, others have since posted sections of the alleged list, including names and postcodes, more generally online.
Canadian police in Toronto said the parent company of the website, Avid Life Media, is offering the reward following "enormous social and economic fallout".
Toronto police acting superintendent Bryce Evans confirmed the force is investigating cases of criminals attempting to extort Ashley Madison clients by threatening to expose them, as well as hate crimes.
"This hack is one of the largest data breaches in the world," he said.
"This is affecting all of us. The social impact behind this leak, we're talking about families, we're talking about children, we're talking about wives, their male partners."
He gave no further information on the two unconfirmed reports of suicide.