Donald Trump has been at loggerheads with many media houses since his election campaign in 2016. He had accused The Times of being a fake media house and criticised it for publishing an investigative report on how he treated women in his private life, alleging that the daily did not carry his version.
A G Sulzberger, 37, recently became publisher of The New York Times after his father Arthur O Sulzberger stepped down.
"The failing New York Times has a new publisher, A G Sulzberger, 37. Congratulations! Here is a last chance for the Times to fulfil the vision of its founder Adolph Ochs 'to give the news impartially, without fear or FAVOR, regardless of party, sect or interests involved'," President Trump said in a tweet.
"Get impartial journalists of a much higher standard, lose all of your phony and non-existent 'sources' and treat the President of the United States FAIRLY, so that the next time I (and the people) win, you won't have to write an apology to your readers for a job poorly done! GL," he said in another tweet.
In a note published yesterday, the new publisher quoted his great-grand-father Adolph Ochs, according to him the vision for the news report was "to give the news impartially, without fear or favor, regardless of party, sect or interests involved".
His vision for the opinion report was to invite intelligent discussion from all shades of opinion, he said.
"This mission feels particularly urgent to me today as I begin my work as publisher of The New York Times. Our society is again being reshaped by political, technological and environmental forces that demand deep scrutiny and careful explanation," he said.
"More than 120 years after Adolph Ochs's vision was printed in these pages, the need for independent, courageous, trustworthy journalism is as great as it's ever been," the new publisher said.
Mr Sulzberger said that the business model that long supported the hard and expensive work of original reporting is eroding, forcing news organisations of all shapes and sizes to cut their reporting staff and scale back their ambitions.
"Misinformation is rising and trust in the media is declining as technology platforms elevate clickbait, rumor and propaganda over real journalism, and politicians jockey for advantage by inflaming suspicion of the press. Growing polarization is jeopardising even the foundational assumption of common truths, the stuff that binds a society together," he added.