By Martin Santa

BRATISLAVA (Reuters) - Thousands of Slovak teachers walked out on Thursday in their biggest strike in almost a decade to demand a 10 percent wage hike, posing a challenge to government efforts to cut spending this year and next.

Officials from the Trade Union of Workers in Education and Science of Slovakia said between 80 and 90 percent of primary and high schools and 30 percent of universities shut their doors as a result of the strike, the largest since 2003.

The teachers' salaries are among the lowest in OECD countries and are also below the average wage in Slovakia, the second poorest country in the euro zone.

Teachers' pay averages 687 euros ($890) a month, according to second-quarter data from the statistics office, while the average worker makes 793 euros.

Teachers say they are often forced to seek jobs on the side to supplement income. It is also quite common for parents to be asked to contribute to school costs, although education is free under Slovakia's constitution.

But their pay demands coincide with Prime Minister Robert Fico's efforts to cut the country's budget deficit below the European Union's threshold of 3 percent of economic output next year.

Pavel Ondek, head of the teachers' unions said by standing firm teachers could push the government into talks. "With a successful strike we can open these doors for sure. If not, we will be forced to play harder," he wrote in a letter to teachers.

33-year-old Bratislava teacher Ivana Sabonosova said: "It is not only about financial reward, this is also about status in society."

Education minister Dusan Caplovic told reporters that the wage demands should be reasonable and consider the government's obligation to deliver on austerity.

The minister said the issue of teachers' low pay had existed for many years and could not be fixed in just four or five months. Caplovic said he personally could envisage that average salaries could go up to 1.2 times Slovakia's average wage by 2016. He said the government wanted an agreement and would talk to the unions.

Prime Minister Fico has promised to fix public finances by taxing the rich while protecting the poor in the central European country of 5.4 million.

His center-left cabinet last month approved a new labor code that gives workers more status and job protection, and has focused austerity measures on the better off by hiking taxes on high wage earners and companies and introducing levies on banks.

Slovakia is expected to be the euro currency bloc's fastest-growing member this year thanks to booming car exports.

But the government has admitted it needs to do more cut the deficit next year to 2.9 percent of gross domestic product from a forecast 4.6 percent gap this year.

(Additional reporting by Radovan Stoklasa; Editing by Jason Hovet and Jane Merriman)