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The English Football League say "difficult decisions will have to be made".
The EFL met with the Premier League and the Professional Footballers' Association on Friday to discuss the "growing seriousness of the Covid-19 pandemic".
Football is currently in shutdown and won’t be restarted until May, at the earliest.
This week the FA agreed to terminate football at all non-league levels below the National League.
Those playing between steps 3-6 (including the Isthmian League and the Southern Counties East) have had their records expunged. There will be no promotion or relegation at that level.
There has yet to be a decision made over the future of the National League, the level below the EFL, but their season could also be about to end.
Whether the EFL go the same way, or play behind closed doors, are options that the governing bodies could consider.
The statement said: “The Premier League, EFL and PFA agreed that difficult decisions will have to be taken in order to mitigate the economic impact of the current suspension of professional football in England and agreed to work together to arrive at shared solutions.
“The leagues will not recommence until 30 April at the earliest. They will only do so when it is safe and conditions allow.
“Further meetings will take place next week with a view to formulating a joint plan to deal with the difficult circumstances facing the leagues, their clubs, players, staff and fans.”
Managers of the Kent sides affected by the decision to terminate non-league have been having their say after being denied the chance of promotion.
The chairman of then-Southern Counties East Premier Division leaders Beckenham Town has expressed his frustration at the lack of communication before a decision was made.
Gillingham chairman Paul Scally this week said that despite the growing financial problems caused by the current crisis, his staff will be paid in full for March.