The ethnic Hungarian minority in Cluj, Transylvania's capital, had feared that the city's Romanian authorities intended to remove the statue completely.
On Thursday, scuffles broke out near the monument, which dominates the main square in Cluj, between policemen and Hungarian demonstrators, who included priests.
The Hungarian government protested against the excavation, a project that had been encouraged by Cluj's mayor, Gheorghe Funar, the leader of the ultra-nationalist Party of Romanian National Unity (PRNU).
Hungarians make up between 1.6 million and 2 million of Romania's 23 million people and are concentrated in Transylvania, ruled by Hungary as part of the Habsburg Empire until the end of the First World War. While Hungarians complain of discrimination in education, culture and other matters, Romanian nationalists argue that politicians in Budapest and the Hungarian minority in Transylvania are scheming to reincorporate the region into Hungary. Four people were killed when clashes between Romanians and Hungarians broke out in the town of Tirgu Mures in March 1990.
Mr Funar, who was elected mayor of Cluj in February 1992 on a platform of making Romanians 'masters in their own house', has banned the public display of Hungarian-language signs and restricted the use of Hungarian in schools. Last year he ordered a Romanian-language inscription to be placed on the statue of King Mathias.
Mr Funar had supported the archaeological dig in an apparent attempt to demonstrate that the ancestors of modern Romanians had preceded Hungarians in Transylvania. While this theory is dear to many Romanians, including former Communists who hold power in Bucharest, the government's decision to postpone the dig underlined its suspicion of Mr Funar as a political rival playing the Romanian nationalist card.
King Mathias was born in Cluj, known as Kolozsvar in Hungarian, in 1440 and reigned from 1458 to 1490. The son of a Romanian nobleman, he became known as Mathias the Just and is remembered by Hungarians as one of their greatest kings.
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