Mr Williamson resigned as a minister yesterday after the New Zealand Herald revealed he had contacted police over the investigation into domestic violence charges against Liu.
In an interview on Campbell Live last night, Mr Williamson talked about he and Liu having neighbouring holiday homes in Pauanui.
He said he recommended the home to Liu when it went on the market, and had used the house while he was making repairs to it over Christmas.
"I'm a fan of being a handyman and the house was good to be able to use while we were doing it," he told Campbell Live.
This morning, Mr Williamson said last night's comments had been incorrect.
"We don't use his holiday home at all. I did some work in it over the Christmas break for the first time ever because he's just bought it," he told Newstalk ZB.
"It was a mistake to say that."
"My kids didn't use it. I had keys to it so I could do some cabling. I said I used it while I was doing some work in it."
Mr Williamson maintains he made a mistake in calling the police over Liu's case, and had no ulterior motive in making the call.
"All I was wanting to know was, was the proceedings going to continue.
"I believe that I made a mistake, I've stepped down as a minister, but I intend to contest the next election and the people of Pakuranga will choose whether they think that's suitable," he told Newstalk ZB.
A Herald investigation today reveals Liu's citizenship ceremony was held in Mr Williamson's electorate office, the day after he was granted the status of a New Zealander.
But the MP rejected accusations that he had allowed Liu's wealth, donations or friendship to influence his judgment.
Mr Williamson said he believed he was doing his job as an MP when he contacted a police superintendent to inquire about two domestic violence charges laid against Liu in December.
He had been "shocked" at the charges because Liu had required a clean record to get a New Zealand visa.
Asked why he told the superintendent about Liu's large investments in New Zealand, he said it was to provide "background" for police. But he admitted that he had made an error in judgment.
"There is clearly a perception that a Member of Parliament should not call the police at all about a case and I will make sure I will never do that again."
He was "shattered" and "gutted" about his demotion to the backbenches and his family were "in a bit of tatters".
Prime Minister John Key was in no doubt that Mr Williamson had "crossed the line" by contacting the police about the Liu case.
"There's no grey in this. In the end there's a line. The line says that ministers do not involve themselves in police prosecutions, because constabulary independence runs at the heart of the New Zealand judicial system. Ministers cannot, in my opinion, make phone calls when there's an ongoing prosecution, whatever the motivations.
"The minute he made the phone call, in my view, he crossed the line."
Mr Williamson vowed to hang on to the Pakuranga seat he has held for 27 years.
He has already been chosen as National's candidate in the electorate, which he retained in 2011 with one of the largest majorities in the country - 13,800 votes.
He could have new competition. Conservative leader Colin Craig and Act Party leader Jamie Whyte have both expressed interest in standing there.
Dr Whyte, who grew up in Pakuranga, said last night he had new confidence after yesterday's events.
