Snowy Valleys Council has asked the NSW Premier to put limits on the newly restored freedom to travel due to fears it will bring coronavirus into the region.
Cr Geoff Pritchard, a retired surgeon, said last week's decision to allow up to two people to visit homes of friends or family risked people travelling or returning to the Snowy Valleys from virus hotspots in Sydney.
"It would almost be like another Ruby Princess [cruise ship] disaster if you had people wandering around the countryside," he said.
"People who want to go travelling should have a test and have their journey recorded for contact tracing in one way or another."
The Snowy Valleys has recorded just one positive test for coronavirus and that person has recovered.
Cr Pritchard said the council area's older population was at higher risk from coronavirus.
"At my age, If I got coronavirus it would be a death sentence," he said.
"I know it sounds heavy saying things like that but that's how serious it is."
Snowy Valleys Council wrote a letter to Premier Gladys Berejiklian asking to "restrict visits to the local region only" and to "not allow overnight stays".
The Premier's office was contacted for comment but did not respond prior to publication.
Other Riverina council mayors have said they will not follow the Snowy Valleys' example, preferring to trust that people will not travel if they have flu-like symptoms.
Wagga mayor Greg Conkey said the city, as a regional capital, would instead have to manage the risk of large numbers of people making essential visits.
"We service a wide-ranging area around the city ... something like 380,000 people access our health facilities," he said.
"Whilst I understand Snowy Valleys' point of view, the Premier has deemed that people can travel provided it's only two people.
"There has been a call for different rules in Sydney, Newcastle, Wollongong and rural and regional Australia; I think that would be unworkable."
Cootamundra-Gundagai mayor Abb McAlister said his council area was already exposed to outside essential workers and visitors via Hume Highway traffic.
"I know what [Snowy Valleys] are saying, with people coming in to see friends or family could be bringing in COVID-19," he said.
"I have got no issues with it from our point of view, because I know a lot of people went from this area to see family they haven't seen for five or six weeks and it's just luck of the draw.
"If we want to open things up, we're going to have to start gradually doing these things."
Temora mayor Rick Firman said the issue of travel risks hadn't been raised in his council.
"We haven't heard that mentioned in council or without council," he said.
"That's not to say that some people might be fearful of that, and to be frank I haven't thought about it in those terms.
"I'm also mindful that we don't want to be too quick to relax as we haven't even been through winter and if you give people an inch, some will take 20 miles."
Wagga MP Joe McGirr, who also received a copy of Snowy Valleys' letter, said he did not support a hard limit on travel distances.
"Lots of elderly people in Wagga have been in social isolation and have relatives in different parts of NSW," he said.
"Those people have appreciated visits and people I have heard from have kept up social distancing during those visits."