Cameron Smith called for the NRL to suspend the competition on Sunday, allowing time to assess the impact of coronavirus rather than reacting "daily or hourly" to the ever-changing situation.
Smith was part of the Melbourne Storm team that recorded an 18-4 triumph over Manly Sea Eagles in the opening round of the 2020 campaign.
However, the former Australia captain feels continuing to play is not the best course of action in the midst of the pandemic, given the amount of travel involved for the teams.
"If we make a decision to suspend the comp for a couple of weeks then I think it just gives everyone an opportunity to actually sum up the situation a little bit better rather than being reactive daily or hourly," Smith said in quotes appearing on the NRL's website.
"We want to be playing rugby league. We'd love to be playing. But this is a serious thing that's happening at the moment.
"I'm really confident with the measures we're taking as a club, particularly from our CEO Dave Donaghy and our doctor to minimise the risk around our organisation and anyone getting the virus or being around large crowds.
"This is a view of our entire team. Given our team travels a lot. We're travelling virtually every second week of the competition so we're going to be exposed to airports, air travel and large crowds a lot.
"Our players aren't concerned about themselves, they're concerned about their families and making this issue which is already global, making it much bigger than what it is in Australia at the moment."
All round two fixtures are to be staged behind closed doors after the federal government declared a ban on non-essential gatherings of more than 500 people due to COVID-19.
Smith is willing to carry on playing in empty stadiums for now, with Melbourne due to face Cronulla Sharks next Saturday in Sydney.
"Going into round two, there's no crowds so we're not going to be around large crowds. So I'm comfortable with where things are at the moment," Smith said.
"If I wasn't comfortable I wouldn't have come up this weekend and the rest of the players wouldn't have come up either. But this thing changes all the time."