Pötsch, 64, was finance director at VW until now and is seen as the favoured candidate of the powerful Porsche and Piëch families, each owners of large parts of the VW business.
Some in the company had criticized the appointment of a long-time insider to the head of the board, who might conceivably bear some responsibility in the firm's plot to outwit regulators' emissions testing using a software "defeat device".
According to dpa sources, there was concern about Pötsch's appointment from the government of Lower Saxony, which holds a 12.4 percent stake in VW and 20 percent of the voting rights.
In a statement on Thursday, VW said that the investigations following the emissions scandal would take "at least a few months".
It wasn't realistic to "arrive at well-founded answers that correspond to the justified expectations of the shareholders within a few weeks," the statement continued.
"I assure you that I will give you answers," Müller wrote in a separate letter to shareholders.
"For that I ask you nevertheless to give me time to completely understand the background."
VW has already set aside €6.5 billion to deal with the fallout of the emissions scandal.
That money will likely be used to refit cars fitted with the infringing software.
But there are likely to be large numbers of compensation claims from customers and shareholders over the company's actions.