Fr Peter West, who has more than 3,000 followers on Twitter and 9,000 on Facebook, describes himself in his Twitter bio as a Catholic priest at St John's Church and "a Russian agent personally assigned by Vladmir Putin to stop Hillary Clinton."
The priest regularly uses Twitter as a platform and has previously described Hillary Clinton as an "evil witch" and former President Barrack Obama as a "bum".
On 29 January, Fr Peter called moderate Islam a "myth".
The Catholic priest has been labelled a "hatemonger" by some on Twitter and in December 2016 Fr Peter said that someone had lodged a complaint against him to the Archdiocese.
In a statement to NJ.com, an Archdiocese representative Jim Goodness said: "Certainly, a priest doesn't give up his civil liberties when he is ordained, and he maintains the same right to freedom of expression as anyone else in the United States," Goodness said. "That said, we are concerned about Father West's comments and actions, and will be addressing them according to the protocols of the Church."
Fr Peter told LifeSiteNews posts about radical Islam were made "on what you might call feminist grounds".
He added: "I'm not dissenting from any teaching of the Church. I consider myself a faithful Catholic. I may have some opinions that diverge from that of some of the bishops. I have promised in the future that I'm not going to take a position on anything that's contrary to the stated positions of my ordinary."
An online petition describing Fr Peter as a "courageous and remarkable priest" who has the "courage to speak truth" has gained 440 signatures.