The dossier includes a number of salacious claims about the Trump campaign's ties to Russian officials, including allegations about Mr Cohen that have not been verified.
BuzzFeed responded with a Twitter post saying the dossier continues to be the subject of investigations by Congress and intelligence agencies, was shown to two U.S. presidents and described in detail by news outlets worldwide.
The salacious and unproven claims in the "Trump dossier" have been used against President Trump and his associates to accuse them of colluding with Russian Federation to influence the 2016 presidential election.
"Even though Defendant Buzzfeed expressly acknowledged the unverified (and potentially unverifiable) nature of the Dossier's allegations, BuzzFeed published the un-redacted Dossier and the Article anyway - without attempting to determine the veracity of these reports with Plaintiff himself", Cohen's lawsuit alleged. "Their actions are so malicious, despicable and reckless, one can only presume that their motives were intentional". Trump and his surrogates have also attempted to cast the document as a partisan attack, noting that a lawyer representing Hillary Clinton's campaign and the Democratic National Committee retained Fusion GPS for research services that began in April 2016. It was presented to two successive presidents, and has been described in detail by news outlets around the world. "We look forward to defending the free press and our First Amendment rights in court".
Last week another attorney working for Trump personally, Charles Harder, sent a cease and desist letter to the publisher and author of the new book "Fire and Fury: Inside the Trump White House", seeking to stop further distribution.
"A year of government inquiries and blockbuster journalism has made clear that the dossier is unquestionably real news", said Smith.
The Steele dossier was comprised of 17 different intelligence reports written by former British intelligence officer Christopher Steele and believed by many as one of the prime motivating factors in launching the FBI's investigation into alleged ties between the Trump campaign and the Kremlin, as well as the ongoing probe by special counsel Robert Mueller, dubbed on Twitter as "the single greatest Witch Hunt in American history" by the president.
It comes amid that the Federal Bureau of Investigation received intelligence from a "voluntary source" in Mr Trump's circle in 2016.
Mr Trump has slammed the dossier as "bogus" and denies his campaign colluded with Russian Federation. Smith also dismissed media "traditionalists" who accused him of publishing "fake news".
Fusion GPS similarly faces several lawsuits related to its work on the dossier.