"I am not at the club's disposal from the beginning of the summer," Veh, who had joined before the start of the season, told reporters. "Because of the current situation I will not be there as coach."
The former VfB Stuttgart and VfL Wolfsburg coach has had a mediocre debut season in Hamburg, with his team in seventh place just outside the European spots after 25 games.
He said his decision was not linked so much with what happened on the pitch but how the club dealt with internal difficulties.
"You need order. What kind of order do we have at the moment? I thought with a new sports director there could have been a new start. But not like that," Veh said.
Former European Cup winners Hamburg, who have not won a major title in 24 years, had been looking for a sports director for almost two years before signing Chelsea's Frank Arnesen late last month to join them from next season.
But the Hamburg board is still split over several other issues, including an embarrassing rejection from German soccer federation sports director Matthias Sammer who turned down the job after Hamburg had announced the deal was all but sealed.
"Basically the club is without leadership at the moment. Bringing in Arnesen was a good thing but there is no unity (in the board) to use this move efficiently."
"I have the impression it is sometimes not about football what is going on here," said Veh. "But we still have nine games to secure a European spot."
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