"I withdrew on March 19 from the presidency of the SDC and made it clear that I will not return until they rescind the March 17 declaration," he said, referring to an announcement by Kurdish and allied groups of a "federal region" in northern Syria.
Manna, an Arab, was co-president of the SDC, an alliance formed in December as the political branch of the Kurdish-Arab fighting force known as the Syrian Democratic Forces (SDF).
The SDF have cleared Islamic State group jihadists out of swathes of territory in northern and northeast Syria and receive air support by a US-led coalition.
Both the SDC and SDF are dominated by Kurdish factions.
Signup to our newsletter and follow us on Facebook and Twitter!
On March 17, Kurdish parties, including the powerful Democratic Union Party (PYD) and their allies, announced the creation of a "federal system" in northern Syria.
Kurdish parties already operate a system of three "autonomous administrations" in Syria's north, with independent police forces and schools.
The federal system would unite those cantons together under a single administrative unit.
But the announcement was heavily criticised by Syria's opposition, including Manna, who called it "counterproductive".
Syria's conflict erupted in March 2011 with anti-government protests but has since morphed into a multi-front war drawing in regional powers.