The team's Autumn Nations Cup opener against Les Bleus was cancelled at the weekend after five players tested positive for the coronavirus.
Additional tests were carried out late last week after a player - understood to be centre Semi Radradra - returned a positive test last Tuesday.
Pacific Rugby Players CEO Aayden Clarke said the Fiji team took all the necessary precautions.
"What's happened inside the camp, although extremely unfortunate timing, is just a sample of what's happening in society at the moment," he said.
"With this virus we really can't predict the pathway that it's taking. I know the protocols and the systems that the team tried to put in place were very much trying to avoid this but sometimes that just can't be done."
The Fiji squad is currently self isolating in their hotel rooms at their tournament base in Saint-Galmier. Like their original training camp in Limoges, they won't be able to interact with each other until they return two negative Covid tests.
Aayden Clarke said officials have not yet identified how the players contracted the virus.
"Obviously a really challenging situation for the players that we've just been keeping tabs with in the camp, having to go back to individual isolation in rooms," he said.
"[These are] extremely competitive athletes that are really preparing well for this test match and overcoming the disappointment that it's not going to happen. You've just got to have the right mindset and be able to adapt to it and that's exactly what the boys are doing."
Fiji Rugby CEO John O'Connor said morale in the camp remained high but there was frustration the team was unable to kick off their Nations Cup campaign.
"Our medical team with the support of the FFR medical team have started contact tracing and are monitoring the players. Further tests are planned for Monday and Wednesday, prior to the Italy match," he said in a statement released at the weekend.
"Everyone, however, understands that the life, safety, and welfare of everyone involved is always paramount and the priority. With Covid-19 the 'new normal' the andemic has thrust upon us life is full of uncertainties and challenges which we have to deal with."
A decision on whether Sunday morning's test against Italy in Ancona goes ahead will be made later this week, with medical and tournament staff working hard to get the outbreak under control.
Aayden Clarke said it was a tough situation with players testing positive at different times.
"It's just a day by day thing for the team and for FRU and all the players at the moment," he said.
"We've all got aspirations to see international rugby and we want to see the Flying Fijians out there doing their things against Italy but public safety and everything that applies to the rest of society does so within this team as well and the players are aware of that.
"They're just going to go through the best possible steps that they can and then make a call when they can."