Audi said on Friday that it would retrofit diesel engines with software that would lower emissions. The upgrade, which would be free for consumers and cover as many as 850,000 vehicles outside the United States and Canada, would reduce emissions beyond legal requirements, Audi said. It added that it was “convinced that this program will counteract possible bans on vehicles with diesel engines.”

A day before Audi’s announcement, BMW said it would offer to upgrade the software in more than 350,000 vehicles. The BMW chairman said the company believed “there are more intelligent options than driving restrictions,” referring to the European cities — including Munich, where BMW is based — that have considered banning or restricting diesel vehicles.

Daimler announced on Tuesday that it would modify three million Mercedes vehicles in Europe to reduce their diesel emissions. None of the companies described the moves as recalls.

European carmakers have heavily promoted the use of diesel vehicles in Europe and the United States to help meet rules on carbon dioxide emissions. But the nitrogen oxides that diesel engines emit are considered carcinogens, and can cause asthma. The cost to automotive companies of installing equipment to neutralize the fumes emitted by diesel vehicles is also increasing, making it difficult to keep the price of the cars competitive.