Lowy said he hoped the discussion would result in fans returning to grounds to support their club.
"We're certainly hopeful of getting the fans back to the game, but it's not just up to the fans, it's up to the outcome of very constructive discussions that will start to take place," he said after the meeting.
"There will be discussions around [ending the boycott]. FFA will be coming to this meeting with a spirit of goodwill and an open mind and with a purpose of solving this issue over the longer term through a very serious and consultative process.
"That consultative process will include active discussions with the fans.
"But having said that, if there are some shorter term issues that can be dealt with swiftly, we're certainly committed to do that."
Lowy attempted to take further heat out of the conflict by acknowledging the FFA had made errors in their management of the issue. A list containing 198 banned A-League fans was made public in Sydney's Sunday Telegraph more than a fortnight ago.
Since then, fan groups have raised other issues including a lack of an appeals process and overbearing policing and security at matches. The contracting of an anti-terror security firm to monitor groups and the FFA's failure to defend fans from perceived media attacks have heightened their ire.
"With the benefit of hindsight, maybe it could have been dealt with a bit earlier, but I stressed at the last press conference that it is a complex issue and these issues are obviously very difficult to deal with," Lowy said.
"But with the benefit of hindsight, it feels we could have dealt with it earlier and better. It's a complex issue and complex issues often don't have clear solutions.
"Having said that, had we had our time again, I think we would have dealt with it differently and more speedily. But we're dealing with it now and we're very pleased we're in a position to engage with the active fans."
The Yellow Fever have walked a fine line over the issue due to the Phoenix's long-term license to play in the A-League being in jeopardy and the Wellington-based club having to keep its crowds up as result. But they still attended Wednesday night's fan group meeting.
"We're very hopeful that with face-to-face dialogue, airing of the issues and understanding of the complexities, we have no other desire than to get the fans back to the game and to do it quickly," Lowy said.
He added that there was a unanimous view among club chairmen.
"What I can report is that the club chairman and myself really want to resolve this," he said.
"We understand the issues, we don't have differences between us and we're very hopeful that with good, sound engagement with the active fan groups, we'll be able to resolve this."
