The country’s foreign ministry confirmed the men were among the eight killed when a truck driver ploughed through crowds on a cycle path in Lower Manhattan.
The group had been celebrating the anniversary of their graduation from Polytechnic College in the city of Rosario in central Argentina.
They were fulfilling a promise made to each other three decades ago, according to reports in Rosario.
The Argentine government expressed its “sincere condolences”, confirming the deaths of Hernan Diego Mendoza, Diego Enrique Angelini, Alejandro Damian Pagnucco, Ariel Erlij and Hernan Ferruchi.
New York terror attack – in pictures
A sixth Argentinian man with the group named as Martin Ludovico Marro was being treated at the Presbyterian hospital in Manhattan.
The government statement added: “The consulate general continues working in permanent contact with the police authorities and the hospital that received the affected, as well as with the relatives in Argentina.
“We accompany the families in this terrible moment of deep pain, which all Argentines share.”
Police said a man drove a rented Home Depot truck on to the cycle path on West Street at around 3pm local time (7pm GMT) and at least 11 other people were injured.
The driver, who has been identified by law enforcement officials as Sayfullo Saipov, 29, from Uzbekistan, was shot by police after jumping out of the vehicle with what turned out to be two fake guns and shouting “Allahu Akbar”.
According to reports in Argentina, the five victims were part of a group of 10 people. Of them, four were unharmed and communicated with their families in the aftermath of the attack – the deadliest in New York since 9/11.
The rented truck mounted a cycle path in Lower Manhattan (REUTERS)
One of the members of the group – Ariel Erlij – paid for the trip for two of his former classmates, who could not afford the cost of the tickets, reports said.
Argentina’s president Mauricio Macri tweeted “Profoundly moved by the tragic deaths this afternoon in NY. We are at the disposal of the families of the Argentinian victims”.
The country’s foreign minister Jorge Faurie said that his heart was with the family and friends of those who had died “at this moment of deep and inexplicable pain”.
A Belgian national was also among those killed in the attack.
The country’s deputy prime minister and foreign affairs minister Didier Reynders said on Twitter: “I am deeply saddened to announce a Belgian victim in Manhattan – I express my condolences to the family and friends.”
Heavily armed police stand guard near the scene in Lower Manhattan (AP)
It later emerged Saipov had been working as an Uber driver after passing a background check, according to a spokeswoman for the app.
In a statement, the firm added: “We are horrified by this senseless act of violence. Our hearts are with the victims and their families. We have reached out to law enforcement to provide our full assistance.”
The suspect was taken to hospital and is in police custody. Officers said his injuries are not life-threatening.
Bikes could be seen strewn across the path in the aftermath of the attack (AP)
In a statement President Donald Trump praised the actions of the first responders and tweeted that the incident “looks like another attack by a very sick and deranged person”.
The president also tweeted: “We must not allow ISIS to return, or enter, our country after defeating them in the Middle East and elsewhere. Enough!”
The terrorist group has not claimed responsibility for the attack.
Mr Trump later said on Twitter he had ordered the Department of Homeland Security to step up its already “extreme vetting” programme, adding: “Being politically correct is fine, but not for this!”
Meanwhile the UK Foreign Office has said it is standing by to provide assistance to any Britons affected by the atrocity.
A spokesman said: “We are in contact with the local authorities and stand ready to provide any assistance but are not aware of any British citizens involved as yet.”
New York terror attack: What we know so far
Prime Minister Theresa May tweeted that she was “appalled by this cowardly attack”, adding: “My thoughts are with all affected. Together we will defeat the evil of terrorism. UK stands with £NYC.”
Mayor Bill de Blasio of New York described the attack as “a particularly cowardly act of terror” that was “aimed at innocent civilians going about their daily lives”.
New York governor Andrew Cuomo said it was a “lone wolf” attack, and there was no evidence it was part of a wider plot.