Time Warner rejected the cash and shares offer and said it had no interest in further talks but sources told the New York Times that 83-year-old Mr Murdoch was determined to make a deal.
New York-based Time Warner said: "The board is confident that continuing to execute its strategic plan will create significantly more value for the Company and its stockholders and is superior to any proposal that Twenty-First Century Fox is in a position to offer."
It also said there were "considerable strategic, operational and regulatory risks" to such a merger.
Mr Murdoch's firm said: "Twenty First Century Fox can confirm that we made a formal proposal to Time Warner last month to combine the two companies.
"The Time Warner board of directors declined to pursue our proposal. We are not currently in any discussions with Time Warner."
Time Warner's holdings include cable channel HBO, maker of True Blood and Game of Thrones, as well as news broadcaster CNN and Warner Bros, owner of Harry Potter, Batman and The Hangover.
The company was in 2001 the subject of the biggest and most disastrous deal of the dotcom boom when it was taken over by AOL in a 182 billion dollar transaction, but the firms later went their separate ways.
Time Warner has since shed a number of its business including publisher Time Inc.
Twenty-First Century Fox includes Fox News and the Fox network behind The Simpsons and Family Guy, as well as Hollywood studio Twentieth Century Fox, maker of the X-Men and Ice Age films. It also owns a large chunk of BSkyB.