Yesterday it was revealed Labour MPs on the committee voted against allowing Brady to make a submission on foreign interference in elections.
Huo said this was a procedural decision.
The closing date for submissions on the inquiry was in September last year – Huo said the date was widely publicised by committee staff in the usual way.
But that was before the committee and Justice Minister Andrew Little decided that the issue of foreign interference was going to be the focus of the inquiry.
"The next step, in my opinion, is to decide whether we should reopen the submissions and invite anyone who's interested in making a submission to do so," he said this morning.
"I would personally welcome a submission from Professor Anne-Marie Brady."
He is also inviting anyone else who would like to make a submission on interference in elections to submit too.
Yesterday Smith said he and the other three National members of the eight-member committee all supported letting Brady submit.
Smith went to the media with his concerns, telling the Herald: "If the committee is going to do its job for Parliament, we need access to both government officials but also New Zealand's most published author on the subject".
Huo today said Smith should follow the process and argue for the submission to be opened rather than "grandstanding via the media".
He would not comment when asked if Smith had breached privilege by taking the information to the media yesterday.
Smith said he welcomed Huo's "change of heart".
"It was an appalling look for Labour to be blocking New Zealand's leading academic on the issue of foreign interference in one's democracy."
Smith claimed the only reason Huo had changed his mind on this issue was because he had highlighted the hypocrisy of Labour members blocking the move.
"If I had not raised the issues publically, Professor Brady would not be being heard and the Justice Select Committee would not be able to do its job."
Professor Brady has been approached for comment.