The former Australia opening batsman had been asked to continue until the 2007 World Cup in the West Indies.
"But I declined" he said. "I didn't want to stay that long. There is no other reason."
Marsh, who has been in the job two-and-a-half years, added: "I have nothing lined up. I will just go fishing and see what happens."
Marsh has refused to get embroiled in the controversy surrounding Zimbabwe cricket in the last six weeks following the sacking of former captain Heath Streak and the strike of white professionals which followed, refusing to comment on the affair in public.
When asked by one of the rebels why he did not support them he responded by saying he was contracted to coach the Zimbabwe national side, insisting: "And that's what I am doing."
Marsh, who will not be involved in coaching ahead of the England tour to Zimbabwe in late October, suggested former West Indies batsman Phil Simmons could be called up as his successor.
Simmons has been in Zimbabwe for the past several weeks coaching at the Academy in Harare.
"I'll be very happy to work with him until he takes over" he said on Sunday.
Simmons played 26 Tests for West Indies. The chief executive of the Zimbabwe Cricket Union Vincent Hogg declined to comment on Marsh's resignation nor whether they had approached Simmons to take over.