The resignation marks a sharp reversal for the FFK, which on Friday issued a firm rejection of calls from players and sponsors to reinstate Advocaat.
The FFK said Rutten’s departure followed "open and constructive" talks between the coach and federation president Gilbert Martina. The federation noted that while Rutten was not the direct subject of internal dispute, he chose to step down to protect the squad’s professional environment.
"A climate that damages healthy professional relationships among players and staff must not be allowed to emerge," Rutten was quoted as saying in a federation statement on social media. "It is prudent to step back. Time is pressing and Curacao must move forward."
Advocaat, 78, led the Caribbean island to historic World Cup qualification last November but stepped down in February to care for his daughter, who was suffering from a serious illness. Rutten was then appointed as his replacement.
Dutch media reports on Monday suggested that Advocaat is now open to a return following improvements in his daughter's health.
The veteran coach, who would become the oldest manager in World Cup history if he travels to the tournament, is backed by a significant portion of the dressing room, reports said.
A press conference has been scheduled for Tuesday to provide further details on the transition.
Curacao begin their World Cup campaign with a Group E match against Germany in Houston on June 14.