Aodhán Ó Ríordáin reacted after the newspaper apologised if the article gave the impression that the victims were to blame.
It also accepted that some of the language in the news report published on Tuesday “could be interpreted as insensitive”.
But Mr Ó Ríordáin took to Twitter to rubbish the apology.
“Your attempt at an apology for your offensive Berkeley article is pathetic. It’s clearly futile appealing to your better nature,” he said.
And in a reference to the gay marriage vote last month, he said: “We are so proud of our young people, at home and abroad. They made history for us last month and we have lost so much this week.”
We are so proud of our young people, at home and abroad.— Aodhán Ó Ríordáin (@AodhanORiordain) June 17, 2015
They made history for us last month & we have lost so much this week. #Berkeley
It follows widespread criticism of the newspaper’s report on the accident in California which linked the partying lifestyle of Irish J1 students to the deaths of six young Irish students in Berkeley.
The report claimed the J1 visa programme had become “a source of embarrassment for Ireland”.
Renua leader Lucinda Creighton described The New York Times article as “grotesque” and “despicable”.
“It is truly ghoulish that at a time where sensitivity is required in dealing with the utterly sad plight of families which have to deal with the death of young children that The New York Times, a supposedly reputable media outlet, would launch such a facile assault upon the character and activities of young Irish students,” she said.
In response to questions from the Irish Examiner, The New York Times said the article was a second-day story following a news story on the collapse.
“It was intended to explain in greater detail why these young Irish students were in the US,” its vice president of corporate communications, Eileen Murphy, said.
“We understand and agree that some of the language in the piece could be interpreted as insensitive, particularly in such close proximity to this tragedy.
“It was never our intention to blame the victims and we apologise if the piece left that impression.
“We will continue to cover this story and report on the young people who lost their lives.”
Despite earlier reports, the article has not been removed from its website.
Reporters, Adam Nagourney and Quentin Hardy, who both reported from Berkeley, and Mitch Smith, who contributed from Chicago, wrote: “They come by the thousands — Irish students on work visas, many flocking to the West Coast to work in summer jobs by day and to enjoy the often raucous life in a college town at night.
“It was, for many, a rite of passage, one last summer to enjoy travel abroad before beginning a career.
“But the work-visa program that allowed for the exchanges has in recent years become not just a source of aspiration, but also a source of embarrassment for Ireland, marked by a series of high-profile episodes involving drunken partying and the wrecking of apartments in places like San Francisco and Santa Barbara.”
The report said the birthday party in the Berkeley apartment had been loud and kept neighbours awake, and it outlined the facts of the tragedy before referencing a 2014 column in The Irish Voice which mentioned “the callous destruction unleashed by these loaded Irish students” of a San Francisco home.
In that incident last September, the Irish community subsequently helped repair the damage.
The report also referenced a “work-hard, party-hard lifestyle” and flagged a Facebook page where Irish J1 students often make “requests for house party sites”.
READ MORE: New York Times apologises for Berkeley article .