Trump threatened with a lawsuit earlier on Friday and has, according to documents from a federal court in Florida, taken action in the matter.
Trump is suing Murdoch, his company News Corp, its subsidiary Dow Jones which publishes The Wall Street Journal, as well as two reporters at the newspaper.
The lawsuit concerns the newspaper's publication of a "dirty" letter that Trump, according to the newspaper, sent to Jeffrey Epstein on his 50th birthday, 2003, at the request of Epstein's assistant Ghislaine Maxwell.
Trump has denied the whole thing and attacked Murdoch on social media earlier on Friday.
"I look forward to having Rupert Murdoch testify in my lawsuit against him and his 'shit heap' of a newspaper, WSJ. It will be an interesting experience", Trump wrote on Truth Social.
Financier and billionaire Epstein died in 2019 in jail after being charged with, among other things, sex trade and abuse of a large number of minors over a long period. Maxwell has been sentenced to 20 years in prison for recruiting girls for the abuse.