He said later through a spokeswoman: "Yes there was a disagreement but it was resolved in person between myself and the other party. I'm not aware of any suggestion of a formal complaint."
The spokeswoman said that Nash had not requested to security or the man involved in the argument that they refrain from reporting the incident.
Speaker Trevor Mallard, who along with the Parliamentary Service general manager is responsible for the welfare of those working in the complex, said he was aware of the incident.
"It was over gym etiquette on machine use," Mallard told the Weekend Herald.
"It's not serious enough for security to report up to me. I only know about it because Nash told me earlier this week."
Nash is a regular user of the parliamentary gym.
Last year in March, Nash posted on Facebook a video of himself in the parliamentary gym bench-pressing a 45kg weight in each hand.
The video has since been removed after it was widely made fun of, but Nash posted a different video a month later of him bench-pressing a 50kg weight in each hand.
The video has had 2700 views and is captioned: "Peeni Henare, Wally and Alf - just calling those out who doubted ... all in the name of trying to keep the ageing body in some sort of shape. Hard work on a parliamentary diet."
Henare, who is the Whanau Ora Minister and Community and Voluntary Sector Minister, commented: "Good form bro!"
Another comment called Nash the "Minister for Gains".
"Wally" is Deputy Police Commissioner Wally Haumaha, who has returned to fulltime police duties after months of controversy over his appointment.
"Alf" is National MP Alfred Ngaro, who is also a frequent visitor to the parliamentary gym.
Ngaro made fun of Nash by posting a video of himself bench-pressing 1kg weights amid much faux huffing and puffing, as Northland MP Matt King tried to suppress laughter as he filmed it.
The video has had about 21,000 views and has the caption: "Hey Stuart Nash - you've inspired me! Saw your video last night and thought I'd give it a go in the gym this morning. 3 sets of 1 rep with 1kg - boom! What do you think of my form Nashy?"