"I have nothing against refugees but I'm worried about the lack of jobs and houses in Whanganui," Reweti said.
"My doctor came here as a refugee - he's a good man and I respect him."
Whanganui is poised to become home to 100 refugees a year following an announcement last week that the city would become one of 13 official refugee settlements.
Fallen had taken exception to comments made by Reweti and others on social media which were derogatory towards different ethnic groups and he said some of them were "vile."
Reweti said he regretted comments which he has since deleted and was sorry that other commentators had been so vitriolic.
Both men said their public showing was not about political campaigning and Fallen had no intention of standing for council this year.
"It made it sound as if I am protesting as part of an election bid for this year but I have no plans to stand," Fallen said.
"There is no political motivation - I just strongly object to ill-founded comments about people we haven't met.
"We don't know where the refugees will be coming from."
Reweti said he had not considered standing for election this year either.
"I hadn't thought about standing but maybe I will now."
Mayor Hamish McDouall joined the conversation and said he agrees that housing is a serious concern for Whanganui.
"When I first learned that Whanganui would be a refugee resettlement location, I raised two main concerns.
"I was concerned about trauma, knowing that around 5 per cent of refugees will need psychological support.
"I didn't know if we had enough professionals in the region to support them and I am now assured that we do."
McDouall's other major concern was housing and it remains a top priority.
"I heartily agree with community concerns about the current shortage of housing.
"I am especially concerned about housing for our elderly and I am pleased that we have been able to retain our pensioner housing."
McDouall said pressure on Whanganui housing had escalated in recent years and although housing was a government concern the council wanted to find solutions.
"We have looked at purchasing a building for emergency housing and we have explored
the possibility of a rent-to-buy scheme for tiny houses.
"It is a relatively new problem for Whanganui and there is a lot to work through."
He said that while housing availability in Whanganui had decreased, the availability of new jobs had increased which is a complete turnaround from the situation of five years ago.
McDouall said there will be many positive aspects to welcoming refugees to Whanganui and cited a much-needed boost to local school populations as one of them.