Comcast offered $35 per share for Fox, which the bidder said represents a 19% premium to Disney's offer.
Disney offered 0.2745 shares of its stock for each share of Fox in December, which comes to $29.18 per share based on Wednesday's close. The total value of Disney's bid comes to $52.4 billion, or more than $66 billion including assumed debt.
Fox gained 0.25% to $43.77 after hours, after gaining nearly 8% earlier on Wednesday. Comcast was flat at $32.32, while Disney was flat at $106.31.
The assets include the Twentieth Century Fox film and TV studios and related operations; cable networks including FX Networks, Fox Sports Regional Networks; international networks; Indian satellite TV group Star India; and stakes in National Geographic Partners, Hulu LLC, UK satellite TV group Sky and other assets.
Comcast Chairman and CEO Brian Roberts wrote a letter to the Fox board on Wednesday, expressing his disappointment that Fox agreed to sell much of its film, television and international distribution assets to Disney last December.
"We have long admired what the Murdoch family has built at Twenty-First Century Fox," Roberts wrote. "After our meetings last year, we came away convinced that the 21CF businesses to be sold are highly complementary to ours, and that our company would be the right strategic home for them."
Rupert Murdoch balked at Comcast's offer last year, following the Department of Justice lawsuit in November to block the sale of Time Warner to AT&T.
Roberts noted in his letter that Judge Richard Leon denied the government's suit against AT&T on Tuesday.
"In light of yesterday's decision in the AT&T/Time Warner case, the limited time prior to your shareholders' meeting, and our strong continued interest, we are pleased to present a new, all-cash proposal that fully addresses the Board's stated concerns with our prior proposal," Roberts wrote to Fox's board.
Comcast's bid for Fox is more complicated than AT&T's deal, however.
AT&T's purchase of Time Warner is a vertical merger that combines wireless and pay-TV networks with content production.
Comcast owns content distribution and production through its NBC division. The company's acquisition of Fox would represent vertical and horizontal consolidation.