The law against minority languages in Slovakia is an emotive issue for many
Thousands of ethnic Hungarians have demonstrated in Slovakia, to protest against a new law that limits the use of minority languages there.
The law sets out to encourage the use of Slovak in official business in minority areas.
Slovakia says the move is in accord with European standards, but protestors argue it breaks international laws.
The Hungarian and Slovak prime ministers are due to meet next week, to try to defuse worsening relations.
Around 10,000 people filled the football stadium in Dunajska Streda, in southern Slovakia, on Tuesday to hear speeches demanding that the law be withdrawn.
Some of its most controversial clauses set fines of up to 5,000 euros (£4,300) for those who continue to infringe its provisions, after a written warning.
Slovak must be used in all official contacts, including the police, armed forces, fire brigade, postal services and local government, with a number of exceptions for minority languages like Hungarian.
But "official contacts" are not clearly defined. The impact of the law on cultural events, and on live reports in minority languages on television and radio, is also not clear.
More than half a million ethnic Hungarians live in Slovakia, and many regard the new law as the latest in a series of crackdowns by the Slovak government against their culture.
Peter Pazmany, of the opposition ethnic Hungarian Coalition Party in Slovakia, said the law: "makes no sense... [it] only creates tension between people who have lived peacefully side by side".
The Organisation for Economic Co-operation and Development (OECD) has said the new law respects the rights of minorities, but has noted the concerns and risks related to its enforcement.
Ties between Slovakia and Hungary have long been strained over Bratislava's treatment of its ethnic Hungarians, who make up about 10% of the population.
For its part, Slovakia has previously voiced its distaste over what it sees as efforts by Budapest to promote Hungarian culture within its own borders.
The protests over the new law follow a row last week, when Slovakia barred the Hungarian president from making a controversial visit.
President Laszlo Solyom had planned to visit a part of Slovakia with a large ethnic Hungarian population, to unveil a statue of the first Hungarian king, Saint Stephen.
Slovakian Prime Minister Robert Fico said the plans were a provocation to his nation.
The BBC's Nick Thorpe in southern Slovakia says relations between the two countries are at the lowest point for many years.
Until 1920, Slovakia was part of the Austro-Hungarian empire, and there are still more than half a million Hungarians living there - about 10% of the population. They are mainly concentrated along a strip of land in the south of the country, close to the border with Hungary.