Steven Woolfe is coming under pressure to abandon his Ukip leadership bid following his altercation with a fellow MEP which left the front runner in hospital.
Senior party figures suggested Woolfe's apparent willingness to resort to violence rendered him unfit for leadership.
Woolfe, who is recovering in hospital in Strasbourg, sought to extend the "hand of friendship" to Mike Hookem, the other MEP involved in the confrontation in the European Parliament.
But while Hookem dismissed the incident as a "handbags at dawn, girl-on-girl" scuffle, he insisted he had not thrown any punches and that Woolfe had been the aggressor.
Meanwhile, president of the European Parliament Martin Schultz announced that he is launching an investigation into the conduct of the two MEPs, which could see them suspended from voting and their expenses cut.
"It goes without saying that disrespectful and violent behaviour does not have a place in the European Parliament," Schultz said.
In his first detailed comments on the incident, Hookem said the flare-up arose out of a meeting on Thursday of the party's MEPs to discuss reports that Woolfe had been in talks about defecting to the Conservatives.
In the course of the increasingly heated debate, he said Woolfe had objected to comments he made and, in front of the whole room, told him: "Let's me and you take this outside mano a mano".
Woolfe then removed his jacket and Hookem followed him into an adjoining anteroom.
"When I walked in he approached me to attack me. He came at me, I defended myself. There were no punches thrown, there was no face slapping, there were no digs, there was nothing," Hookem told BBC Radio Humberside.
Following the "scuffle", he said the door to the anteroom then opened again, and Woolfe fell on to an MEP standing in the doorway.
"Some of the MEPs helped him up. He stood straight up, there was no indication of him hitting his head on metal windows or anything else," he said.
His account is at odds with Woolfe, who told the Daily Mail that Hookem "came at me and landed a blow" and that he had then fallen back and hit the door frame.
Hookem said he had been "shocked" when he later learned Woolfe had been admitted to hospital, but he insisted he was not to blame for any injury.
He played down the confrontation, telling Sky News it was "quite silly, quite embarrassing, handbags at dawn, girl-on-girl. It lasted seconds".
However he said that if he is disciplined as a result of an internal party inquiry ordered by interim leader Nigel Farage into the incident, Woolfe should also face action.
"I may be suspended. If they suspend me, they'll have to suspend Steven Woolfe as well. I hope it doesn't come to that. I will fight my corner," he said.
Ukip MEP Nathan Gill, who visited Woolfe in hospital, said he is recovering well but is being kept in for a further 48 hours as a precautionary measure.
He refused to be drawn on whether Woolfe intends to press on with his leadership bid following the shock resignation of Diane James just 18 days after she was elected.
"I think it is way too early for us even to consider that," he said.
But while there is clear relief across the party that Woolfe is recovering, potential rivals are suggesting the incident raises questions over his suitability to lead the party.
Lisa Duffy, who was runner-up in last month's leadership election, said party members were "embarrassed" by what had taken place.
"Do we want a leader who will get himself involved in an altercation, or do we want a leader who is going to be rational and reflect and deal with things in an appropriate manner?
"Violence or any kind of offering to go outside is not the way to deal with problems," she told the BBC Radio 4 Today programme.
Ukip MEP Jonathan Arnott said it is "obvious to anybody" that Woolfe can no longer be a candidate.
"This really portrays Ukip in an appalling light," he told BBC2´s Daily Politics programme.
"The people who have worked hard for this party, year in, year out, they expect better of their MEPs than what has been seen over the last 24 hours."
But any moves to prevent Woolfe - the Ukip migration spokesman - standing in the leadership election will only exacerbate the bitter divisions within the party.
There was anger when he was barred from standing in the last election after it was ruled that he had submitted his nomination papers 17 minutes late.