Southport say they will not play Tuesday's National League North fixture against Curzon Ashton because of a lack of coronavirus testing and the financial impact of the pandemic.
The club claim they have not received any tests from the National League.
In addition, Southport do not want to play while lower-league clubs face the threat of insolvency.
In a statement, Southport said they will not play until "at least the result of the resolution is known".
"We have had concerns, as we have expressed on numerous occasions, as to the health and safety of our players, staff and volunteers who are being asked to play during a global pandemic," the club added.
Southport say they only played their FA Trophy defeat by Torquay earlier in February because the prize money would pay for testing.
Southport are 17th in the National League North table.
In January, the National League North and National League South were suspended for two weeks amid discontent over funding.
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