About 70 percent of VW's 12,300 employees in Slovakia joined the protest, the union said. It began on Tuesday and is the first ever strike at the carmaker's plants in the country.
After two rounds of failed talks earlier this week, union chief Zoroslav Smolinsky said a compromise between his demand of 13.9 percent wage hike over two years and the company's offer of 9 percent could be reached at the next meeting.
The union is also asking for longer lunch breaks.
"We are close to a deal... We hope to return to the table as soon as possible," Smolinsky said.
In the event of a deal, production lines that normally make about 1,000 cars a day - almost all of which are exported - could resume on Monday, he added.
VW produced 388,687 cars in Slovakia in 2016, including the Volkswagen, Audi, Seat and Skoda marques.
The company pays its Slovak workers an average of 1,800 euros a month including bonuses, double the national average but less than half of the 4,200 euros earned by equivalent employees in Germany, according to the union.
Slovak Prime Minister Robert Fico has supported the strike, saying Volkswagen should pay its Slovak workers the same pay as its western European ones.
The Finance Ministry has estimated that 12 days of strike would cut 0.1 percentage point off the country's annual economic output.
Growth is seen at 3.3 percent this year and above 4 percent in coming years, with the auto sector the most important driver. Slovakia, with a population of 5.4 million, produces more than 1 million vehicles a year, making it the biggest per-capita auto producer in the world.
Kia Motors Corp (>> Kia Motors Corporation) and Peugeot (>> Peugeot) also have plants in Slovakia and Jaguar Land Rover [TAMOJL.UL] is due to open one next year.
(Reporting By Tatiana Jancarikova; editing by John Stonestreet)