BERLIN—Volkswagen AG on Tuesday said the chief executive of its luxury brand Audi, jailed in a probe into the car maker’s diesel-emissions cheating scandal, has stepped aside pending clarification of the issues that led to his arrest.
Prosecutors said Rupert Stadler had agreed to cooperate with authorities and that candid testimony could hasten his release.
Mr. Stadler, 55 years old, is the only member of Volkswagen’s executive board to be arrested in connection with the company’s admission in 2015 to rigging millions of diesel-powered cars to cheat emissions tests. He was arrested Monday after prosecutors said they found evidence that he was planning to interfere with the investigation.
After his arrest at his home, Mr. Stadler told prosecutors he wanted to answer their questions as soon as possible, said Stephan Necknig, a Munich prosecutor.
“Mr. Stadler has declared that he was willing to testify,” Mr. Necknig said Tuesday, adding that prosecutors expect to question him during the course of the week.
Volkswagen and Audi declined to comment on Mr. Stadler’s arrest or the investigation against him.
After a meeting of Volkswagen and Audi directors, Volkswagen said in a written statement Tuesday that the directors agreed to temporarily relieve Mr. Stadler of his duties at his own request while he tries to clear his name. Last week, the Munich prosecutor’s office added the executive to a list of suspects in a probe into fraud and illegal advertising related to the emissions scandal.
Volkswagen named Abraham Schot, Audi’s sales chief, as the brand’s interim CEO.
Mr. Necknig said Mr. Stadler could be brought before a judge soon to review the grounds that led to him being detained. Depending on how forthcoming he is in his testimony this week, Mr. Stadler could be released soon, Mr. Necknig said.
“If he is really cooperative, then there would no longer be any danger that he planned to interfere with the investigation. It depends on what he says,” Mr. Necknig said.
Mr. Stadler’s attorney didn’t return a request for comment Tuesday. Mr. Stadler has in the past said he had no prior knowledge that illegal software had been installed on Volkswagen or Audi engines.
Mr. Stadler hasn’t been charged with any wrongdoing. In Germany, it is common practice for prominent individuals suspected of a crime to be named by prosecutors in public. Being named a suspect doesn’t mean the person will ultimately be charged.
Munich prosecutors last week ordered a raid on Mr. Stadler’s home to search for evidence. Mr. Necknig said investigators confiscated documents, computers, telephones and thumb drives, and gathered witness testimony.
Without going into detail, Mr. Necknig said investigators issued an arrest warrant after finding evidence among the seized materials and witness testimony that led them to believe Mr. Stadler would obstruct the investigation.
Mr. Stadler’s arrest thrust Volkswagen into a new management crisis as the diesel scandal engulfs Audi.
Volkswagen admitted in 2015 to rigging nearly 11 million diesel-powered vehicles to cheat on emissions tests, including models made by Audi. Volkswagen pleaded guilty to defrauding the U.S. government and has incurred about $25 billion in penalties, fines, and compensation for customers stemming from the resolution of civil suits and the criminal charges filed by the U.S. government.
Volkswagen has compensated nearly 500,000 owners of tainted Volkswagen, Audi and Porsche models in the U.S. In Europe, the company hasn’t compensated diesel owners financially but says it has updated the software on nearly nine million diesel vehicles to remove the illegal code that allows the cars to test clean but emit higher emissions on the road.
The U.S. has indicted eight Volkswagen executives, including former CEO Martin Winterkorn, on charges of conspiracy to defraud the U.S., to commit wire fraud, and to violate the Clean Air Act. Mr. Winterkorn has stated publicly that he had no knowledge that Volkswagen vehicles were rigged to cheat. His attorney declined to comment.
In Germany, Mr. Stadler’s arrest marked a turning point in the official investigation of the scandal.
The manager is the highest-level executive to be arrested in connection with the affair, a sign that prosecutors are turning up the pressure in more than a dozen separate investigations by state’s attorneys in three German states.
Prosecutors in Braunschweig, Munich and Stuttgart are pursuing a number of independent investigations of executives and lower-level employees at Volkswagen, Audi AG, Porsche AG, Daimler AG, Chrysler and Robert Bosch GmbH.
The Braunschweig investigations, launched in 2015 after Volkswagen admitted to installing devices in cars aimed at circumventing emission tests, involve 49 suspects in five separate investigations but no one has been indicted, said Klaus Ziehe, a spokesman for the Braunschweig prosecutors.
Heiner Römhild, a prosecutor in Stuttgart, said his office is conducting seven investigations focused on at least 13 suspects. One investigation centers on two employees of Daimler, which makes Mercedes-Benz cars, on suspicion of fraud and illegal advertising for selling cars with high diesel emissions. Daimler declined to comment on the continuing investigation.
Stuttgart is also investigating employees at Bosch, which made the engine-control unit in diesel engines built by Volkswagen and other manufacturers. The investigation is focused on six Bosch employees in Germany on suspicion of aiding and abetting fraud in connection with diesel-emissions cheating at Volkswagen and Audi. The investigation also targets two unnamed suspects employed by Bosch in the U.S. Bosch declined to comment on the continuing investigation.
Volkswagen declined to comment on any of the continuing investigations.
Write to William Boston at william.boston@wsj.com
