Twenty-First Century Fox says Walt Disney Co has raised its offer for Fox assets to US$38 per share, topping Comcast Corp's US$35 a share offer last week.
The new Disney offer, which would be in cash or stock divided proportionately, is about US$10 higher than Disney's first bid in December 2017.
Disney's latest offer is "superior" to the proposal made by Comcast, Fox said in a statement.
"We are extremely proud of the businesses we have built at 21st Century Fox, and firmly believe that this combination with Disney will unlock even more value for shareholders as the new Disney continues to set the pace at a dynamic time for our industry," said Rupert Murdoch, executive chairman of 21st Century Fox.
"We remain convinced that the combination of 21CF's iconic assets, brands and franchises with Disney's will create one of the greatest, most innovative companies in the world."
Disney and Comcast are battling to win Fox's movie and television studios at a time when legacy media and distribution companies are looking to expand to better compete with younger media firms like Netflix that sell their content directly to customers.