A turbulent week for Europe's biggest automaker started when Piech, who has long been the company's key powerbroker, was quoted last Friday as telling Der Spiegel magazine he was "at a distance from Winterkorn."
That surprised observers and prompted fevered speculation about the position of Winterkorn, 67, Volkswagen's CEO since 2007. Winterkorn's contract runs until the end of next year.
Winterkorn "is the best possible" chief executive for Volkswagen, Friday's statement from the six-strong executive committee of Volkswagen's 20-member supervisory board said. Piech is part of the committee.
It added that the body "places great importance on the fact" that Winterkorn "will pursue his role ... with the same vigour and success as before, and that he has the full support of the committee in doing so."
The committee will propose extending Winterkorn's contract at a board meeting next February, it said, without specifying how long the extension may be.
The 78-year-old Piech, himself a former CEO, didn't specify last week what his issue with Winterkorn was, though experts have pointed to concerns about profitability at the core Volkswagen brand and a disappointing market share in the U.S. as possible factors.
Winterkorn has received backing from the head of Volkswagen's influential employee council, while the governor of Lower Saxony state, a minority shareholder, criticized the public discussion about the company's leadership. Union and employee representatives make up half of major German companies' supervisory boards.
The Piech and Porsche families together control a majority of shares in Volkswagen. Board member Wolfgang Porsche said in a statement Sunday that Piech's comment about Winterkorn represents "his private opinion" and wasn't cleared with his family.
Volkswagen shares initially rose on Friday's news but closed 1.1 per cent lower at 235 euros ($251.66). Frankfurt's DAX index of blue chip stocks was 2.6 per cent lower overall.
Also Friday, Volkswagen said it delivered 2.49 million vehicles worldwide in the first quarter, 1.8 per cent more than a year earlier. Sales in Europe rose 4.1 per cent and deliveries in China were up 2 per cent, but U.S. sales declined 1.4 per cent.