"This would be detrimental to our NHS (National Health Service) and other government-funded services," the Professional Footballers' Association said in a statement.
Taking on the Premier League as a whole, the PFA said the 20 million pounds being given to the NHS by the world's richest soccer competition was "welcome, but we believe it could be far bigger."
The union's strident stance came after further talks Saturday involving clubs and the league as Liverpool became the latest Premier League side defying political anger by using a government bailout scheme to furlough some non-playing staff.
Health Secretary Matt Hancock had told players at clubs furloughing staff to take a pay cut. Sports minister Nigel Huddleston reminded the Premier League to ensure it "helps the national effort."
Liverpool, which leads the league by 25 points, followed fellow 2019 Champions League finalist Tottenham, Bournemouth, Newcastle and Norwich in furloughing staff.
Under a job retention scheme implemented to help businesses survive the national lockdown, staff can be put on furlough and receive 80% of their salaries from the government, up to a maximum of 2,500 pounds ($3,000) a month.
Liverpool said it would top up salaries to ensure staff still received the full amount but that still means using public funds to pay some staff. Former Liverpool defender Jamie Carragher called that a "poor" move, saying "respect and goodwill is lost" by the club.
The European champions have been owned for a decade by John Henry's Fenway Sports Group, which also features the Boston Red Sox.
Liverpool made a pre-tax profit of 42 million pounds on a turnover of 533 million pounds last year and it said "complex" talks continue with players about savings on salaries.
A meeting of Premier League clubs on Friday had ended with agreement on the need to ask players to see 30% of their pay cut or deferred. But the standoff between the players' union and clubs continues.
"The players are mindful that ... the combined tax on their salaries is a significant contribution to funding essential public services - which are especially critical at this time," the PFA said in a statement.
"Taking a 30% salary deduction will cost the Exchequer (treasury) substantial sums." If the season cannot be completed, the Premier League could owe broadcasters a reported 762 million pounds. Burnley, which has nine of its 38 games remaining, estimates a cash shortfall of 50 million pounds.
The union raised the prospect of a lengthy spell without games. Reducing pay by 30% over a year equated to 500 million pounds, the PFA said, claiming the government would lose out on more than 200 million pounds in tax.
"What effect does this loss of earning to the government mean for the NHS?" the PFA statement continued.
"Was this considered in the Premier League proposal and did the health secretary, Matt Hancock, factor this in when asking players to take a salary cut?"
The PFA said players would still like "precise details of our commitment" settled, recognizing a need to help their clubs, non-playing staff, lower-league sides and the health service.
"However, to achieve a collective position for all Premier League players - of which there are many different financial and contractual circumstances from club-to-club - will take a bit more time," the union said.
There are moves to cut costs at the English game's governing body, the Football Association, with the national teams unable to play and the FA Cup suspended. Broadcaster Sky Sports reported Saturday that England manager Gareth Southgate had agreed to a 30% pay cut.
"The financial implications of the coronavirus are not yet known however, as a not-for-profit organization, we want to ensure that we take the appropriate course of action to support the wider organization and our employees," the FA said.
"We will make a further announcement on our next steps in due course."
Like many other countries, Britain is in effective lockdown, with schools, bars, restaurants and many businesses shut to help slow the spread of the new coronavirus.
The government's latest data on Saturday showed 4,313 people with COVID-19 have died in British hospitals, an increase of 708 on a day before.
The coronavirus causes mild or moderate symptoms, such as fever and cough, for most people. But for others, especially older adults and people with existing health problems, it can cause severe symptoms like pneumonia. AP KHSKHS