The cable and broadband giant Comcast said on Thursday it was abandoning its bid to acquire a major chunk of 21st Century Fox but would continue its push to win control of the British satellite broadcaster Sky, a move that ended a complex bidding war for Rupert Murdoch’s media company.

In a statement, Comcast said it “does not intend to pursue further the acquisition of the Twenty-First Century Fox assets and, instead, will focus on our recommended offer for Sky.”

Comcast had been locked in a battle with the Walt Disney Company for the bulk of Mr. Murdoch’s Fox empire, with the cable company submitting a $65 billion offer for the assets last month. But Disney brushed back Comcast’s offer with a higher bid of $71.3 billion, which Mr. Murdoch and his board quickly accepted. Shareholders for both Disney and Fox will vote on the proposed merger on July 27.

The cable giant had already started to move off a Fox deal a few weeks ago to focus on acquiring control of Sky, which, with more than 23 million customers across five countries, is one of Europe’s most prized media companies. Comcast had initially been drawn to Fox primarily for its international holdings, which include a 39 percent ownership stake in the satellite TV service. Now Comcast and Fox are bidding for the other 61 percent of the company.