But the investigation into the alleged confrontation will continue, although Parliamentary authorities have little power to punish MPs even if they are found to broken the rules.

Andrews government minister John Eren and right-wing factional chieftain Adem Somyurek issued a public statement on Friday to say that the matter was over in their minds following an apology by Mr Somyurek.

"We have now resolved our differences. Adem has apologised for the colourful language he used which caused John offence and John has accepted," the statement read.

It is understood that the two men came to an agreement after meetings between their staff members rather than a settlement being imposed by the party leadership.

The pair also denied claims, aired by the opposition during Question Time on Thursday, that Mr Eren had been drinking when the clash occurred.

"It is important to note that we categorically reject that alcohol played any part in this," the MPs said.

"Neither of us are interested in pursuing a complaint against each other in relation to that evening and now consider the matter is closed."

The parliament's presiding officers, speaker Colin Brooks and upper house president Bruce Atkinson, announced on Thursday there will be an internal investigation into the incident.

The two MPs argued heatedly inside Strangers, the members-only restaurant inside Parliament House, on Wednesday night.

Mr Somyurek had previously sent Mr Eren a string of angry text messages sprayed with foul language, including threats of "payback" towards federal Labor MP Richard Marles.

"I'm going to f___ that Marles," he texted.

"Better not see that c___."

Mr Somyurek, an upper house MP and former minister in the Andrews government who was forced to stand down over bullying claims, is leading an attempted factional realignment that has stirred up rancour inside the Victorian Labor Party.

Mr Somyurek and Mr Marles are rival factional leaders within the Labor right and Mr Eren is closely aligned with Mr Marles.

On Friday, Mr Marles laughed off the threats and abuse he was subjected to by Mr Somyurek.

"Colourful character assessments are part and parcel of the business that we are in," Mr Marles told Sky News.

It is unclear where the controversy leaves Mr Somyurek's factional power - his negotiations stalled recently, with key unions and their Parliamentary blocs refusing to be part of his proposed new order.

Labor's national leader Bill Shorten, who has been reported to be cautiously supportive of Mr Somyurek's plans, described reports of the clash in Parliament as a distraction.

Campaigning in Preston on Friday for next month's byelection in the federal seat of Batman, Mr Shorten said he did not accept that he had been supportive of Mr Somyurek's factional push.

"I'm not going to get distracted - if other people want to focus on their own arguments, then that's up to them," Mr Shorten said.