"Michael Barbaro, the author of the now discredited" The New York Times "hit piece on me with women, has in past tweeted badly about me. He should resign," Trump tweeted.
The weekend report based on interviews with several women who worked with Trump in the last few decades portrays the 69-year-ol real-estate tycoon in a negative light.
The report said that the thrice-married Trump has a mixed history with women, with crude remarks mixed with efforts to foster the career of female employees.
Trump has denied the allegations and has been critical of the daily both on Twitter, other social media platforms and in his interviews to other media outlets.
One of the lead woman in the story - a former girlfriend of Trump - has alleged that the Times "spun" her quotes.
The Times said it stands by its story.