Nathan Gill, a fellow member of the European Parliament, says doctors want to keep Woolfe in hospital for 48 more hours "as a precaution".
Steven Woolfe suffered seizures and needed brain scans after he collapsed following a "physical" confrontation at a heated meeting of UKIP's European Parliament members (MEPs) in Strasbourg to discuss the party's future.
A handout picture released by ITV NEWS on October 6, 2016 shows UK Independence Party MEP, Steven Woolfe, lying face-down on a walk-way inside the European Parliament building in Strasbourg in eastern France.
In an interview with BBC Radio Humberside, he "categorically" denied throwing any punches at Woolfe and insisted he was not responsible for his injuries.
BBC political correspondent Tom Bateman said the meeting followed Steven Woolfe's recent praise for Theresa May's premiership and an admission he had "flirted with the idea" of joining the Conservatives but chose to stick with UKIP. A source told New Europe that Woolfe was struck by UKIP MEP Mike Hookem. "A bit of a scuffle", he said.
"I then said "No Steven, you had 20 days to get this in".
Mr Oakden said the events did not characterise or define UKIP, adding: "The party is far bigger than any one individual".
Woolfe, who had been supported by both Farage and Arron Banks, the party's main financial backer, was quick to throw his hat into the ring to replace James on Wednesday. I never punched him.
UKIP leader Nigel Farage said there was an incident in the party room meeting right before Mr Woolfe lost consciousness.
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Speaking to the BBC's Newsnight programme, the UKIP chairman said the incident appeared to be a case of "two individuals who clearly got carried away" but it would be inappropriate to speculate over what caused Mr Woolfe to fall.
In a statement from hospital, Mr Woolfe said he still had numbness in his face but was "feeling brighter, happier, and smiling as ever". Earlier, he told the Daily Mail that Hookem "came at me and landed a blow" after they left the meeting room.
Nigel Farage, who is now the party's interim leader, has also ordered and investigation into what happened.
Thursday's incident came a day after Woolfe had declared his candidacy to become permanent leader of the anti-EU party.
Woolfe had announced his intention to run in an upcoming leadership contest and was bookies' favorite to win.
Roger Helmer, one of the UKIP MEPs at the meeting where the altercation occurred, said there had been "a lively exchange of views".
Mr Woolfe was the first contender to throw his hat in the ring having been barred from standing in the last leadership election after it was ruled he submitted his nomination papers 17 minutes late.
Woolfe, 49, annoyed some party colleagues when he said recently that he had considered joining Britain's governing Conservatives.
Mr Hookem said he would co-operate fully with any investigation into the incident by his party.