Volkswagen AG said it has approval to repair most of its rigged European diesel engines and made a deal with U.S. regulators to resubmit questionable software for review in 85,000 other vehicles, signs of progress in its effort to overcome the two-month-old emissions crisis.

German automotive regulator KBA has approved a software update for 2.0-liter diesel motors and has agreed in principle to a plan for 1.6-liter engines, Chief Executive Officer Matthias Mueller told about 1,000 company executives Monday in Wolfsburg, Germany. The costs and complexity of the fixes, which apply to more than 90 percent of the affected vehicles in Europe, are "manageable," he said in excerpts of the speech obtained by Bloomberg.

The U.S. Environmental Protection Agency and California Air Resources Board agreed to let Volkswagen seek approval for a revised version of software in 85,000 diesel engines that had been targeted in the latest probe by U.S. regulators, the company said. Assuming it is approved, the fix should cost in the mid-double-digit millions of euros, Volkswagen said.