The New York Times article, said to be written by a White House official, says Mr Trump's own appointees are trying to stifle his agenda.
Fierce speculation surrounds who was responsible but a spokesman for Mr Pence denied it was him.
Mr Trump described the writer as "gutless" and the newspaper as "phony".
"The vice president puts his name on his op-eds," tweeted Jarron Agen, Mr Pence's communications director and deputy chief of staff.
"The @nytimes should be ashamed and so should the person who wrote the false, illogical, and gutless op-ed. Our office is above such amateur acts."
The theory that Mr Pence wrote the article largely stems from the use of the word "lodestar", a term meaning "star that leads or guides" and one which the vice-president has frequently used.
In the New York Times piece, published on Wednesday, the author refers to the late Republican Senator John McCain as a "lodestar for restoring honour to public life and our national dialogue".
Another senior White House appointee, Secretary of State Mike Pompeo, also fiercely denied he wrote the editorial, attacking both writer as a "disgruntled deceptive bad actor".
"I come from a place where if you're not in a position to execute the commander's intent, you have a singular option, that is to leave," he said.