Adds background on search lawsuit in paragraph 3, share movement in paragraph 7

May 6 (Reuters) - The U.S. Department of Justice has proposed that Google sell its AdX digital ad marketplace and DFP platform for managing and delivering ads on websites, after a federal judge found the company illegally dominated two online ad-tech markets.

The proposed remedies, including divestitures, are necessary to end the Alphabet-owned tech giant's GOOGL.O monopolies and restore competition in the ad-exchange and publisher ad-server markets, the DOJ said in a court filing late on Monday.

U.S. District Judge Leonie Brinkema in Alexandria, Virginia last month found Google liable for "willfully acquiring and maintaining monopoly power" in those two markets. The ruling was another blow for Google after a separate judge found last year that Google held an illegal monopoly in online search.

Brinkema 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.

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.

Shares of Alphabet were down nearly 1.1% in premarket trading on Tuesday.

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.

(Reporting by Abinaya Vijayaraghavan; additional reporting by Chandni Shah in Bangalore; Editing by Nivedita Bhattacharjee, Mrigank Dhaniwala, Miyoung Kim)

((Abinaya.V@thomsonreuters.com;))