FRANKFURT, Sept 19 (Reuters) - Germany's top financial regulator has called problems affecting customers at Deutsche Bank's Postbank unit "unacceptable", two weeks after the agency issued an unusual rebuke of the lender.

Deutsche, Germany's largest bank, began acquiring Postbank, with its millions of clients and roots in the country's postal system, in 2008 during the global financial crisis, but for years struggled to complete its integration.

Deutsche said in July it had completed a final phase of the integration, but two weeks ago, the regulator BaFin said it had seen "considerable disturbances" at Postbank.

They included disruptions in online offerings, difficulty in reaching customer service and long processing times. BaFin said it would "take relevant supervisory measures if appropriate".

BaFin's chief Mark Branson has now further scolded Deutsche Bank's handling of the matter.

In an interview with Germany's Sueddeutsche Zeitung published on Tuesday, Branson called the issue "unacceptable and extraordinary".

"I would even say it's an unprecedented situation when we look at how many complaints there are about a single institution," he was quoted at saying.

He called on bankers to fix the problem quickly.

Deutsche Bank apologised to customers for the inconvenience and said that it was working on a number of solutions.

(Reporting by Tom Sims, Editing by Friederike Heine)