Jackson Hope's account of the incident supports the public statements of the former Liberal leader, who has said the only words spoken between the two men came when the attacker asked for a handshake and then swore at him after the headbutt.
Abbott told Macquarie Radio Mr Jackson Hope briefly grappled with the man, before he "scarpered off, swearing".
Prior to the arrest, police described their suspect as a man with short, spiky, sandy-coloured hair and facial piercings, who had been wearing a leather jacket with a "Yes" badge at the time of the incident.
The incident happened after Abbott attended a private function in the Tasmanian capital on Thursday afternoon.
A photo from Abbott's press conference this morning appear to show a small mark on his bottom lip.
"It was very disconcerting to find ... someone who under the guise of wanting to shake your hand gives you a so-called Liverpool kiss," Abbott said.
"As he was scuttling away, amid all the F this and F that, was 'you deserve it because of all the things you've said'. I think it was pretty clear it was ... politically motivated violence."
After her interview with Jackson Hope, Sky News presenter Samantha Maiden said there was "nothing to suggest this has anything to do with same-sex marriage other than those eyewitness reports" from the former prime minister and his staff member that the man was wearing a badge that said "Yes".
Abbott is a fervent campaigner of voting "No" in the marriage equality postal survey and travelled to Hobart this week seeking a voice in an increasingly noisy and divisive national debate.
And with a brazen assault on him by a headbutting tattooed "Yes" supporter he seems to have found it.
Abbott did not have any obvious physical injury to his face when he appeared before the media this morning but has said he was left with a swollen lip immediately after the headbutt.
This morning it emerged there may be CCTV footage of the attack after a spokesman for Custom House Hotel told news.com.au they did have cameras outside the building, which is close to where Abbott was assaulted.
However they said they had not had a chance to check them to see whether the fight had been captured on film.
In a press conference in Hobart, a Tasmanian police spokesman said: "Hobart detectives are investigating this matter and we urge the attacker to come forward and give himself up."
"Tasmanian police would like to reiterate that violence of any form in the community is unacceptable," the spokesman said.
Police are also seeking CCTV or video evidence of the alleged attack.
Anyone with information about the alleged incident including evidence in the form of video footage or closed circuit television footage was urged to call Hobart Police or Crimestoppers.
On Thursday night Abbott contacted Sky News Bolt Report programme to inform them of the incident before he had even spoken to local police.
The story has dominated national media and allowed the Member of Warringah the national platform he has been craving.
Speaking outside a Hobart waterfront hotel this morning Abbott said he was "sorry to say" the "love is love" campaigners were the ones spreading the hate.
"There's not much coming from that (No) side," he said.
He lashed former Labor prime ministers Kevin Rudd and Julia Gillard who had previously voted against marriage equality in parliament.
"Now, it seems if you speak out for a concept of which has stood since time in - of marriage - you risk being headbutted in the street. Now, it's pretty sorry that that is where Australia is and this is one of the many reasons I say we should think long and hard before going down this path."
Abbott said he wanted all Australians to be "decent and kind and caring and loving" to gay friends and family, but that didn't mean they needed to be allowed to marry the traditional way.
"It doesn't mean that we have to agree with the activists and change a definition of marriage ... from which so much else flows. Because it is marriage which gives us families, it is families which give us communities, it is communities which are the building blocks of our nation. You change the definition of 'marriage' and you just don't know what else comes in its wake," he warned.
"Look, it is a shock - it is a shock to have a fellow Australian seeking to shake your hand turn a handshake into an assault. It is a shock. Normally a handshake is a sign of trust and peace. It is a sign of two people wanting to deal openly and courteously with each other, but this handshake turned into a headbutt.
"I think it's sad that this debate has come to that and my plea to everyone in the remaining weeks of this debate is to keep it courteous, keep it respectful, but above all else, respect the values, the institutions with that have shaped us since the beginning of our journey and which I think should continue to shape us as we move forward as one cohesive country."
Tasmanian police contacted Mr Abbott about the incident after he spoke to a reporter about it on Thursday night. However this morning Mr Abbott told reporters a staff member had alerted the AFP after the incident.
Abbott said his attacker "wasn't very good at" headbutting but the blow did make contact.
"The only damage was a very, very slightly swollen lip," he said. Abbott did not require medical attention.
