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 Mr Woolfe's apparent willingness to resort to violence rendered him unfit for leadership.
North West England MEP Mr 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 Yorkshire and North Lincolnshire MEP Mr Hookem dismissed the incident as a "handbags at dawn, girl-on-girl" scuffle, he insisted he had not thrown any punches and that Mr Woolfe had been the aggressor.
Meanwhile, European Parliament president Martin Schultz announced that he was launching an investigation into the conduct of the two MEPs, which could see them suspended from voting and their expenses cut.
Mr Hookem said reports that he punched the MEP were incorrect. He told the Press Association: "That's totally wrong. I never touched him, never hit him, never punched him, never slapped him or anything else I've been accused of doing."
Mr Hookem said the flashpoint came when Mr Woolfe said he had been kept off the leadership race ballot paper.
"I said, 'Sorry Steven, I disagree with that, you never got your paperwork in. You had 20 days to get your paperwork in, you failed to do it. It's as simple as that. You're at fault, nobody else, not the party, not the NEC, you're at fault'.
"He then took umbrage at that."
Mr Hookem said Mr Woolfe told him: "Well if that's the tone of this meeting, maybe me and you should take it outside the room, mano-a-mano."
He said Mr Woolfe then picked up his jacket and went out of the room.
"So I went out of the room into this small anteroom where he came at me. And what occurred was a tussle. Nothing happened. It was literally seconds because the other MEPs followed us in there.
"The door opened. I backed off. Steven fell through the door and I went back to sit back down again."
Mr Hookem said Mr Woolfe jumped up and said he only wanted to talk to him.
"I was backed up because my colleague Paddy O'Flynn said, 'No, sorry Steven, you were the one that instigated this, you were the one that stood up and said let's take this outside mano-a-mano'.
"He was the one that did it, it wasn't me. It was him that said this.
"I have to say there were no punches thrown from him or me. I never hit him, I never slapped him, I never pushed him.
"So what occurred later on in that day had nothing whatsoever to do with me."
His account is at odds with Mr Woolfe, who told the Daily Mail that Mr Hookem "came at me and landed a blow" and that he had then fallen back and hit the door frame.
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?" she told the BBC Radio 4 Today programme.
"Violence or any kind of offering to go outside is not the way to deal with problems."
Ukip MEP Jonathan Arnott said it was "obvious to anybody" that Mr Woolfe could 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."