FRANKFURT (Reuters) - Car factories across Germany were at a standstill on Friday as industrial workers staged a third day of 24-hour strikes, focusing on plants owned by Mercedes-Benz (>> Daimler), Porsche, Audi (>> Volkswagen) and BMW (>> Bayerische Motoren Werke).

The full-day walkouts, due to end late on Friday, are IG Metall's last warning shot before votes are cast on whether to take extended industrial action that could cost German companies hundreds of millions of euros in lost production.

Both the union and employers have said they are open to resuming talks on Monday, but they have each insisted that the other side must show more willingness to make concessions.

With Europe's largest economy in robust health and unemployment at record lows, the country's biggest union is demanding an 8 percent pay rise over 27 months for 3.9 million workers in the metals and engineering sector.

The union has also asked for workers to be given the right to reduce their weekly hours to 28 from 35 to care for children, elderly or sick relatives, and to be able to return to full time after two years.

Employers have offered a 6.8 percent wage increase, but rejected the demand for shorter hours unless they can also have the flexibility to increase workers' hours when necessary.

They have also dismissed the idea that they should make up some of the pay shortfall for workers who cut their hours.

Half a million workers have taken part in the three days of strikes this week, IG Metall said, hitting production at almost 280 companies including large companies such as Daimler (>> Daimler) and Airbus  (>> Airbus SE) but also dozens of smaller suppliers of products used in the production of cars, aircraft and machinery.

The union has targeted the automotive sector in particular.

Germany is home to around 1,000 car and car parts makers, accounting for roughly 10 percent of Europe's biggest economy and relying heavily on a well-oiled supply chain of components.

It was not immediately clear how big the loss of production was for the affected companies.

"Now it is up to the employers to understand the signal we are sending and make a significant improvement to their offer. If the employers are willing to do that, talks can resume on Monday," IG Metall chief Joerg Hofmann said.

The head of the national employers' association had told German TV station ZDF earlier on Friday that he hoped the conflict could be resolved early next week.

Reiner Hoffmann, head of Germany's association of labour unions, said he expected other unions to follow IG Metall's example and fight for more flexible working hours in upcoming negotiations, according to German weekly Spiegel.

Germany's second-biggest union, Verdi, is expected to publish its wage demand for the public sector on Feb. 8.

Verdi and IG Metall together account for about 15 percent of the German workforce, and other sectors tend to broadly follow their agreements.

(Reporting by Maria Sheahan; Editing by Edwina Gibbs and Alison Williams)

By Maria Sheahan