NEW YORK — One of the key stewards of the Federal Reserve’s unconventional monetary stimulus is parting ways with the central bank, a move that stunned Wall Street and left large shoes to fill in its all-important market trading section.

Brian Sack, head of the markets group at the Federal Reserve Bank of New York, has tendered his resignation, according to a release Thursday from the New York Fed. Sack, 41, will stay in his current post until June 29, when the Fed’s latest monetary stimulus program, known as Operation Twist, is set to expire. He will then be placed on leave until Sept. 14, during which he will have limited contact with the bank, the release said.

The departure comes as debate grows over the future of the ultra-easy monetary policy pursued by the Fed since the 2008-09 financial crisis. Investors and bond dealers are now intently questioning whether the Fed is prepared to embark on a third bond-buying program to boost the economy or is preparing for an eventual unwinding of those policies to tighten monetary conditions.

With the economy improving, the question remains whether growth can remain sufficiently healthy without further monetary support while threats to the economic and investment climate continue from sources such as the euro zone’s sovereign debt crisis.

“I’m dumbfounded,” said Raymond Stone, co-founder of Stone & McCarthy Research Associates, which closely tracks Fed policy. “He laid the groundwork for a lot of things the Fed has done and communicated clearly to the market. He did an excellent job in a difficult environment.”