"It's really important for our members' health and safety that they get tested, and for the safety of the wider public.
"The penalty side of it, we would like to see that as the absolute last resort."
Barclay said employers and officials should take a constructive approach, continue to encourage people to get tested and make it easy for them to do so rather than resorting to the punitive side.
"Our members have always been willing as far as I'm aware to be tested, he said. "Early on there were barriers in the way for them to get tested.
"At Auckland Airport, for example, the test site was quite a long way away and people were expected to go in their own time.
"To make it available on site and enable people to get tested during work time is a basic really.
"Communication is critical. I think the communication early on wasn't great and our members didn't necessarily understand that they were being encouraged to get out and get tested."
There had been very few cases of the union's members testing positive for Covid-19, he said.
"We're worried about the negative commentary that's out there about managed isolation and quarantine, and also about the borders because I think that's really tough on people working at the frontline.
"Having said that, they also get quite a bit of positive feedback from people going through managed isolation and quarantine."
Prime Minister Jacinda Ardern was confident the testing would take place as required in the latest orders.
Asked on Morning Report if the Government would be making sure this time that the testing was happening, Ardern said "yes".
"We have orders in place, health orders, and of course that means that essentially we're mandating and there are consequences if people refuse to be tested."
It emerged last month that 60 per cent of staff working at the country's borders had never been tested for Covid-19. That was despite the Government instructing the testing of all border staff on a regular basis in late June.
Otago University Professor Sir David Skegg was among health experts who criticised the revelation, saying weekly testing for frontline staff working at the border should have been compulsory as stringent border protection is vital for New Zealand's elimination strategy.