"We have written to Mtutuzeli Nyoka (CSA president), A K Khan (CSA vice-president) and Gerald Majola (CSA chief executive) and urged them to resolve the existing differences within the organisation as soon as possible", said SACA chief executive Tony Irish.
"We have pointed out to them the damage that this ongoing dispute, which is effectively a political one, is doing to cricket," he said.
Nyoka was reinstated as CSA president by the High Court in Johannesburg earlier in April after being "unlawfully" fired by CSA.
He has demanded that the CSA hand over its financial documents as ordered by the court.
CSA earlier agreed to hand over all financial documents relating to bonuses of R4.7m and the alleged disappearance of R68m from the organisation’s coffers.
The bonuses were apparently paid to 40 CSA staff members for work done during the 2009 Indian Premier League (IPL) and the subsequent Champions League.
The missing R68m was in a CSA suspense account, according to an affidavit by Nyoka submitted during his legal action against the organisation.
In rejecting the allegation, CSA said the money had been held on behalf of the Board of Control for Cricket in India (BCCI) for the running costs of the IPL competition hosted by South Africa in 2009.
Irish said the players' stakeholding in the game meant they had a right to speak out when the game's health and reputation was placed in jeopardy.
"SACA and the players have not taken sides in this dispute and, for the most part, have stayed out of it in the hope that the parties involved would deal with it quickly and return the focus to cricket matters.
"This doesn't seem to be happening and an escalated conflict now shows no sign of ending.
"The fact that it is also being played out in the media is embarrassing and damaging for the game," he said.
SACA president Boeta Dippenaar said the dispute was taking place against a background of other serious challenges to the game.
"Players no longer need to play for their country to gain recognition and earn a good living," he said.
"They can play only in the IPL and other T20 competitions around the world for this."
Dippenaar said "all" wanted to see the best players in each country continuing to play international cricket.
"For this to happen, cricket boards need to make cricket played under their administration the best it can be.
"The current controversies in South African cricket are working against this locally."