The financially-stricken club's administrators announced last week that Portsmouth could fold unless more of the squad can be sold off to further reduce the wage bill at Fratton Park.
It is understood eight senior players have yet to reach agreement with the club over unpaid salaries.
Supporters group SOS Pompey handed over an open letter to the players at Portsmouth's Eastleigh training ground on Monday morning in an attempt to make them compromise on their wages, while administrator Trevor Birch fears former owner Balram Chainrai and his company Portpin could pull out of their proposed deal to buy the club if more players are not moved on.
SOS spokesman Bob Beech told BBC Solent: "This is the end game for Pompey, in a couple of weeks it will be over.
"Some players were excellent and stopped to listen to what we said, others as expected weren't interested and drove straight on.
"At the end of the day, they have contracts and they expect those contracts to be paid and that is not an unreasonable stance to take.
"But the well is dry and if they stay and keep their demands going then there will be no club and they will end up with nothing."
In the letter, the fans said they sympathised with the players due to the money they had lost, but urged them to "demonstrate that footballers aren't the shallow, selfish people portrayed in the press".
The letter said: "With everything that has happened you, like us supporters, have every right to be angry, you are as much a victim of the incompetence that has left our club teetering on the brink as anyone.
"Now though, you have the chance to write your name in the history of our club, the decisions that you make will decide whether 114 years of history come to an end."
Israeli defender Tal Ben Haim, reportedly one of the club's highest earners, told Sky Sports News that the club was not in the current situation because of the players.
Ben Haim, who revealed he had lost approximately £2.5million in net wages, said: "We sign contracts in good faith and try to play football, but still we want to help the club to survive."
Administrator Birch told ESPN at the weekend that the club will go out of business within two weeks if an agreement with the players could not be reached.