LONDON — Comcast’s bid to acquire the bulk of 21st Century Fox’s entertainment assets appears to be over. Instead, the cable giant will focus on fighting Fox for control of Sky, one of Europe’s most prized media companies.

The Philadelphia-based Comcast increased its offer for Sky on Wednesday, valuing the satellite broadcaster at $34 billion, or 26 billion pounds. That topped a bid from 21st Century Fox, Rupert Murdoch’s media empire, that came earlier in the day. Fox’s offer valued Sky at about $32.5 billion. Sky’s independent board had already recommended Comcast’s new terms.

But Sky is just one element in a larger, complex corporate showdown. The latest move escalates a war between rival media companies being waged across two continents and involving two different transactions exceeding $100 billion in value in total.

Both the Walt Disney Company and Comcast have bid to buy most of Fox’s entertainment assets, including Sky and another growing international business, Star India, which would help increase their global reach. Now, Comcast is unlikely to continue pursuing Fox and will instead concentrate its efforts on acquiring Sky, the people familiar with the process said.