The US Department of Justice has proposed that Alphabet's Google divest its AdX advertising marketplace and ad server DFP, a court filing showed on Monday, after a federal judge found the company illegally dominated two online ad-tech markets.

The judge set a September trial date on Friday, after hearing from Google and the DOJ on potential remedies for the company's dominance in ad tools used by online publishers.

The Justice Department said the proposed remedies, including divestitures, are necessary to end Google's monopolies and restore competition in the ad-exchange and publisher ad-server markets.

Google has said the company supported behavioural remedies such as making real-time bids available to competitors, but that prosecutors cannot legally pursue a bid to force it to sell parts of its business.

"The DOJ's additional proposals to force a divestiture of our ad tech tools go well beyond the Court's findings, have no basis in law, and would harm publishers and advertisers," Lee-Anne Mulholland, Google's vice-president of Regulatory Affairs, said in a statement to Reuters.

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AdX, or Ad Exchange, is a marketplace where publishers can make their unsold ad space available to advertisers for purchase on a real-time basis. Publisher ad servers are platforms used by websites to store and manage their digital ad inventory.

Along with ad exchanges, the technology lets news publishers and other online content providers make money by selling ads.

Last year, Google took a major step to end an EU antitrust investigation with an offer to sell AdX but European publishers rejected the proposal as insufficient.