Salah, 26, and the Egyptian Football Association have previously been at loggerheads due to a disagreement over image rights.
Now the conflict has flared up again after the striker and his lawyer accused the FA of failing to respond to a list of requests dealing with the player's treatment.
The list of demands has not been made public but Salah's lawyer Ramy Abbas Issa said they involved the player's "well-being whilst with the national team, and assurances that the image rights violations wouldn't happen again".
In an angry rebuttal the football federation said Monday that it would not accept the requests, blasting some as "illogical" and insisting it would not "favour one player over another".
The fresh war-of-words between the two sides comes ahead of Egypt's African Cup of Nations qualifier against Niger on September 8.
The disagreement between national hero Salah and the Egyptian FA first burst into the open in April over the player's image rights.
Salah was angered that his image was being used by the national team's main sponsor, telecoms firm WE, when he already had a contract with rival company Vodafone.
That dispute was eventually resolved following intervention from political leaders.
The player was also reportedly left unhappy after he was made to appear with Chechen strongman Ramzan Kadyrov at Egypt's training ground in the region for the World Cup in Russia this summer.
Kadyrov has been accused of wiping out dissent with a brutal crackdown on his opponents.
Egypt crashed out of the World Cup after losing its three matches, with Salah struggling to reach his best after sustaining a shoulder injury playing for his club Liverpool in the Champions League final.