Motor traffic going through the Phoenix Park should be stopped, according to the Green Party.
The group, which includes two TDs, an MEP and a number of councillors, say the past couple of weeks have shown how vital the park is to the inner city.
They believe the Office of Public Works (OPW), which runs the area, should trial the closure to traffic until schools reopen.
Councillor Michael Pidgeon says it should be a destination, not a route for cars.
"Cars won't be able to use it as part of their commute but instead use it as it was intended to be which is as a park and a destination
"We have seen it's quieter, it's safer for families and it is just a nicer place to be.
"It's a park transformed.
"We think it's something that they could at least trial until the schools reopen, just a few months until and make sure we get a summer of calm."
Cllr Pidgeon said that as social distancing will be staying with us for some time there is a need for people to have somewhere they can do their exercise.
Kevin Carter, chair of the Dublin Commuter Coalition, says the park should be left to walkers and cyclists.
"It just seems like a backwards approach and I think that Dublin City Council is starting to realise that we need more space, not less," said Mr Carter.
"So it doesn't make sense to me to have all the roads that currently in the Phoenix Park remain open."