Comcast said on Monday it had abandoned its bid for most of the assets of Twenty-First Century Fox, leaving Walt Disney as the sole suitor in pursuit of the $40 billion-plus deal.

"When a set of assets like Fox's becomes available, it is our responsibility to evaluate if there is a strategic fit that could benefit our company and our shareholders," Comcast said in a statement. "That is what we tried to do and we are no longer engaged in the review of those assets. We never got the level of engagement needed to make a definitive offer."

Disney's negotiations with Fox are continuing, and a deal could be reached as early as this month, sources close to the situation said on Monday. The persons asked not to be identified because the deliberations are confidential.

Disney did not immediately respond to request for comment. A Fox representative declined to comment.

The assets in question would have expanded Comcast's international footprint through ownership of European pay TV provider Sky and Star network in India. A source told Reuters in mid-November that Comcast had approached Fox about its interest, and talks were in early stages.

Comcast shares were up 1.5 percent in after-hours trading, while Disney shares were up 0.2 percent and Fox shares fell 1.3 percent.

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Disclosure: Comcast is the owner of NBCUniversal, parent company of CNBC and CNBC.com.