Mike Hookem, speaking to the BBC in his first interview since the incident Thursday threw the right-wing UKIP party into turmoil, acknowledged there had been a "scuffle" between him and Woolfe.
But Hookem characterized the encounter, in an anteroom to an office where other UKIP MEPs were meeting, as "grappling," and said it was instigated by Woolfe.
Asked about possible consequences, such as suspension from the party, Hookem said: "I never threw a punch. I never assaulted him. I will stand my corner."
Woolfe collapsed a couple of hours after the incident Thursday at the European Parliament in Strasbourg, France, and remained in hospital Friday.
President of the European Parliament Martin Schulz said he had referred the altercation to the Code of Conduct Advisory Committee for an emergency meeting and asked for it to be dealt with as a matter of urgency next week.
He said reports of the "very regrettable matter" were "extremely serious" and that the incident may breach European Parliament rules on behavior.
"It goes without saying that disrespectful and violent behavior does not have a place in the European Parliament," Schulz said in a statement.
The front pages of several of Britain's national newspapers were dominated Friday by the image of Woolfe apparently sprawled unconscious on the floor at the European Parliament.
Farage: 'Not very seemly behavior'
UKIP has promised a full inquiry into what it called an "altercation," as what exactly happened remains unclear.
Interim party leader Nigel Farage pledged to hold an investigation into the incident. "It's two grown men involved in an altercation," he told journalists in Strasbourg on Thursday.
"It's not very seemly behavior. But I'm not today going to get involved in the blame game and name names. It shouldn't have happened."
"We're talking about a dispute that finished up physically."
In a statement released from the hospital Thursday, Woolfe said he was feeling better. "The CT scan has shown that there is no blood clot in the brain. At the moment I am feeling brighter, happier and smiling as ever," he said.
"As a precaution, I am being kept in overnight awaiting secondary tests to make sure everything is fine."
He thanked hospital staff and his fellow UKIP Members of the European Parliament via Twitter for their care.
According to a statement on his website, Woolfe had "2 epileptic-like fits and numbness on the left hand side of his body" and passed out. However, tests have shown no bleeding on the brain.
"I am sitting up, and said to be looking well. The only consequence at the moment is a bit of numbness on the left hand side of my face," Woolfe's statement said.
UKIP has been riven by infighting since Farage stood down from the leadership, the day after Britain voted by a narrow margin in a referendum to leave the European Union. The party, which has long called for tighter immigration controls and Britain's "independence" outside the European Union, claimed the Brexit vote as a victory.
Woolfe announced on Wednesday his intention to lead the party. He had intended to stand in the original ballot to replace Farage, but failed to submit his nomination papers on time.
The successful candidate, Diane James, stood down after 18 days
, saying she did not have the full support of the party's MEPs and office-holders.
Woolfe, 49, is the Member of the European Parliament (MEP) for North West England, having taken office in July 2014, and is the UKIP spokesman on migration and financial affairs.