LONDON — Comcast and 21st Century Fox will settle their battle for control of broadcaster Sky through a rare auction designed to put an end to months of offers and counteroffers from the American media empires seeking a foothold in the European pay TV market.

The auction will begin after the London stock market’s close Friday and end Saturday evening after a maximum of three rounds of bidding, said Britain’s regulator, the Takeover Panel.

Fox has long been trying to acquire the 61 percent of Sky it doesn’t already own. A bidding war emerged last December, when Comcast made an offer for Fox’s entertainment assets, which Disney is in the process of buying for about $71 billion. Comcast eventually dropped out of that contest to focus on its acquisition of Sky.

The regulator called an auction “to provide an orderly framework for the resolution of this competitive situation.”

For Comcast, Sky’s 22.5 million customers offer a chance for growth – a company with proven quality in sports and entertainment together with the technology to deliver it.

Fox, meanwhile, has long sought to take full control of Sky. Rupert Murdoch’s last bid foundered amid a 2011 phone-hacking scandal.

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