By Nick Thorpe
BBC News, Budapest
Ethnic Hungarians have staged demonstrations against the new law
The prime ministers of Hungary and Slovakia, Gordon Bajnai and Robert Fico, have agreed on measures to defuse a row which is poisoning relations between the two countries.
The talks at a castle in the northern Hungarian town of Szecseny focused on the amended State Language Law which came into force in Slovakia on 1 September. It sets out to strengthen the use of Slovak in minority areas.
Speaking after Thursday's meeting, Mr Fico pledged that "no individual will be fined in Slovakia for using their own language".
Slovaks say the law is necessary to reinforce the speaking of Slovak. Hungarians say that should be done by better teaching, not by law and fines as the new regulations envisage.
Relations between the two countries have deteriorated to the extent that Hungarian President Laszlo Solyom was prevented from paying an unofficial visit to Slovakia on 21 August.
Both countries have now agreed on closer consultations to prevent any repetition of that incident, as well as on police co-operation to combat racism.
At least half a million Hungarians live in Slovakia - 10% of the population.
"When Slovaks come into my shop, of course we speak to them in Slovak," said Eva Takacs, manager of a flower shop in Dunajska Streda, a town in southern Slovakia which is ninety per cent Hungarian.
At this rally ethnic Hungarian children wore traditional dress
"If we make mistakes, they are kind enough to correct us. That's common sense. I don't believe this law will achieve its objective - to destroy the good relations which exist between Slovaks and Hungarians."
From another predominantly Hungarian town, Galanta, a woman working in a hairdressers complained on a Hungarian language website that her Slovak boss had told her she was forbidden to speak in Hungarian to customers from 1 September.
Controversy still reigns over the exact meaning and interpretation of the amended law. The Slovak ambassador to Budapest, Peter Weiss, assured journalists that it only affects public, not private contacts.
But Article 1.5 says specifically that the law applies not only to state and municipal authorities, but also to "legal persons, self-employed natural persons and private individuals".
The Organisation for Security and Co-operation in Europe (OSCE) has also been drawn into the dispute.
Both countries have now accepted that the OSCE will act as adviser and referee in the dispute.
Before Thursday's meeting the OSCE High Commissioner for National Minorities, Knut Vollebaek, issued a confidential "opinion" on the new Slovak law at Slovakia's request.
"The amendments to the State Language Law pursue a legitimate aim and are - overall - in line with international standards.
"Some elements, however, raise or - depending on the implementation - might raise issues of compatibility with international standards and with the constitutional principles of the Slovak Republic," reads a copy of the opinion, seen by the BBC.
It cites more than a dozen criticisms of the law, which were not taken into account by the Slovak parliament when it passed the law on 30 June.
Sources at the OSCE say they believe the Hungarian side are also exaggerating the harmful effects, and that the real test will be in the way the law is implemented.
The Slovak Ministry of Culture, which is responsible for overseeing the law, expects to actually start implementing it from January 2010.
Until the 1920 Treaty of Trianon, Slovakia was part of greater Hungary, and is still known as the Felvidek or "Uplands" to this day.
The region played an important role in the survival of Hungarian culture, and Hungarian kings were crowned in Bratislava during the Turkish occupation of other parts of the country in the 16th and 17th centuries.
In 1993 Slovakia and the Czech Republic became separate countries. In 1999 both joined Nato, then in 2004 the European Union, alongside Hungary, Poland and several other former communist bloc states.
Prime Minister Fico has appealed for national unity for the "defence of Slovakia's national interests".
He accused Slovak journalists of breaking ranks to criticise the law and the way in which the Hungarian president was prevented from visiting the country.