DOJ says Google should spin off Android if it doesn't meet some suggested remedies.

The U.S. Department of Justice (DOJ) said Alphabet's Google (GOOGL) should sell off its Chrome browser, following an August court ruling that the tech giant holds an illegal monopoly in the search market.

The DOJ's amended filing with federal judge Amit Mehta, who made the August ruling, comes a month after it submitted a framework for restructuring Google, including breaking up the tech giant.

"Google's ownership and control of Chrome and Android -- key methods for the distribution of search engines to consumers -- poses a significant challenge to effectuate a remedy that aims to 'unfetter [these] market[s] from anticompetitive conduct' and 'ensure that there remain no practices likely to result in monopolization in the future,'" the 23-page filing said.

The DOJ said that a successful remedy would end third-party payments that disadvantage Google's rivals.

"To address these challenges, Google must divest Chrome, which has 'fortified [Google's] dominance,'" the filing said.

Google Chief Legal Officer Kent Walker said the company will file its own proposals next month, "and will make our broader case next year."

"DOJ's staggering proposal would hurt consumers and America's global technological leadership," Walker wrote.

Losing Chrome, which controls two-thirds of the search market, would be damaging to Google. The tech giant requires the browser to gauge activity from users and use that data to target ads -- its biggest revenue source.

The DOJ also requested that Google face "behavioral remedies" to prevent its control of the Android mobile operating system from disadvantaging others. If Google violates those, it should be compelled to divest Android, the DOJ said.

Alphabet shares, which are up 26% this year through Wednesday's close, are edging lower in premarket trading.