BRATISLAVA (Reuters) - Thousands of Slovak teachers went on strike on Monday, forcing most of the country's schools to close, as they demanded a 10 percent pay rise from the government which is battling to trim its budget deficit.

More than 4,000 teachers gathered in Bratislava waving signs that read "For how long will we educate the nation for a pittance?" and "We give money to Greece, but don't have any for schools".

Teachers in the euro zone's second-poorest country currently earn an average of 687 euros ($890) a month, the lowest in the OECD group of developed nations.

Unions said they had rejected a government offer to pay teachers 5 percent more, half the increase demanded by teachers. Further meetings were scheduled with the government on Tuesday.

"We don't just want higher salaries, we also want to highlight how bad situation is in Slovakia's education sector. It is on the edge of an abyss," Pavel Ondek, head of the teachers' unions, told protesters in the country's capital.

A 5 percent pay rise would cost the government 60 million euros, but still leave an average teacher's salary below the country's mean monthly wage of 793 euros.

Teachers in Slovakia are often forced to seek second jobs to supplement their incomes, and it is quite common for parents to be asked to contribute to school costs, although education is free under the Slovak constitution.

Centre-left Prime Minister Robert Fico won a March election on a pledge to help poorer Slovaks.

While his government decided to raise taxes on companies and the rich in 2013, it has angered some supporters with measures aimed at cutting the budget deficit to below the European Union ceiling of 3 percent of gross domestic product.

Slovakia's economy is expected by the European Commission to grow by 2 percent next year, making it the second-fastest growing country in the bloc next year.

But analysts say the growth, driven by exports of cars produced in the country, would only provide a limited boost to budget revenues.

Union leaders said the strike had shut 80 percent of grammar schools and 70 percent of high schools in the central European country of 5.4 million.

($1 = 0.7717 euros)

(Reporting by Martin Santa; Editing by Michael Winfrey and Sophie Hares)