In a tweet posted during last weekend’s Cape Town Sevens, Ryan, who stepped down from his role after Rio 2016, urged the FRU to start paying the players.
The FRU has responded by releasing a statement, expressing its "disappointment" at Ryan’s "constant remarks" and "ongoing tweets about the performance of the team".
"While, the FRU appreciates Ben Ryan’s contribution to Fiji Rugby and the success we have achieved through his leadership of the sevens team, he has chosen to move on to other challenges which we respect and all have accepted but it seems it is difficult for him to move on," the statement reads.
Englishman Ryan has taken to Twitter again, describing the FRU’s statement as "ridiculously childish".
"I've only said positive things about everyone and one tweet that tells the truth hits a chord," he added.
Welshman Gareth Baber has been appointed as Ryan’s successor as Fiji seek a successful defence of their Olympic title at Tokyo 2020.
Baber is due to assume the post on January 2, 2017, before which head of physical performance Naca Cawanibuka will be in charge.
"The FRU has also appointed a new coach and he will lead the Fiji men’s sevens team moving forward and we all need to give Baber a chance, including Ben Ryan," the FRU statement added.
"It is no longer Ben Ryan’s team and Ben must understand this and he must allow our new coach Baber to deal with the issues in relation to his team.
"All the players that were selected for the first leg of the IRB [World Rugby] Series revolved around Ben Ryan’s extended squad.
"Their employment contracts with FRU expired after the Olympics.
"They, however, have all been paid their relevant allowances while in camp and while on tour for the two tournaments."
The FRU has also denied Ryan’s claims that the national governing body has lost its sponsorship and funding.
"FRU has been having ongoing discussions with the Fiji National Sports Commission and our sponsors in relation to the contracting of our sevens players both men and women," the statement concluded.
Fiji crushed Great Britain 43-7 in the Olympic final at the Deodoro Stadium.
They lost to England in the quarter-finals of the Cape Town Sevens yesterday, a week after losing to South Africa in the final of the Dubai Sevens.
Since leaving his post as Fiji coach, Ryan has been performing ambassadorial and advisory roles.