Volkswagen announced Wednesday that its top executives were willing to accept "sharp reductions" in their annual bonuses as the embattled carmaker struggles to stem the fallout from its massive engine-rigging scandal.

"The supervisory and executive boards are in agreement that given the current situation, a signal should be sent regarding the issue of management board pay," VW said in a statement.

"Various models are currently being discussed which will represent a suitable and fair solution for everyone," the statement continued.

"In consequence, this will lead to a sharp reduction in the variable remuneration," it said.

The details will be agreed at a supervisory board on April 22 and published in VW's annual report on April 28, the group added.

Earlier the regional state premier of Lower Saxony, where VW is based, had announced that board members were willing to accept "sharp cuts" in their annual bonuses.

"Already in November, chief executive Matthias Mueller expressed an expectation that belts would have to be tightened," prime minister Stephan Weil told the regional parliament in a regular update on the VW scandal.

The state of Lower Saxony is a major shareholder in VW, which is based in Wolfsburg, and is the biggest employer in the region. As a representative of the regional state government, Weil holds a seat on VW's supervisory board.

"This is in line with the opinion of the regional government, which believes a clear signal is needed on this matter," Weil said.

Debate is currently raging in Germany over whether VW executives are morally entitled to the performance-related bonuses for 2015.

- Still incalculable costs -

CEO Mueller had been quick to prescribe belt-tightening to the carmaker's 600,000-strong workforce in the wake of a global scandal that erupted six months ago when it emerged that VW had installed emissions-cheating software into 11 million diesel engines worldwide.

The costs of the scandal are still incalculable but are expected to run into many billions of euros (dollars) as a result of fines and lawsuits.

Mueller's predecessor, Martin Winterkorn, who quit as soon as the scandal broke last September, was the highest-paid executive in Germany for a number of years, earning around 15 million euros per year.

Of his total salary of 15.8 million euros in 2014, 13.9 million euros were bonuses.

The other board members pocketed bonuses of between four and seven million euros in the same year.

According to the weekly magazine Der Spiegel, the former finance chief Hans-Dieter Poetsch, who was appointed to the head of the supervisory board in October, pocketed nearly 10 million euros as "compensation" for the lower pay he would receive as a result of the switch.

But VW insisted that Poetsch, too, was willing to take a cut.

The sharp reduction "will also be the case for Mr. Poetsch -- at his own wish," the carmaker said.

State premier Weil said he "greatly welcomed" Poetsch's gesture.

VW, which is expected to post a loss running into many billions of euros for 2015, could also announce a waiver in the dividend payout to shareholders for the first time since the early 1980s.

The carmaker, which has annual sales of more than 200 billion euros, is normally generous to its German employees and paid them a bonus of 5,900 euros for 2014. It has promised another bonus for 2015, but has not yet said how much it could be.