The Cypriot Government has condemned an attack by Greek Cypriots on a group of Turkish Cypriots who tried to visit their old home on the Greek side of the divided island.
Greeks have not been to the Turkish side since 1974
The attack, in the southern port city of Limassol, came as thousands of Greek and Turkish Cypriots continued to cross the island's dividing line for the first time in nearly 30 years.
Justice Minister Doros Theodorou described the attack as "unacceptable and dangerous" and said such incidents would not be tolerated under any circumstances.
The decision to ease the restrictions, taken by the Turkish Cypriot authorities, has been cautiously welcomed by the Greek side.
However, the Greeks blame the Turkish Cypriots for the failure of the peace process which would have led to the reunification of the island prior to EU membership in two years' time.
Meanwhile, Turkish Foreign Minister Abdullah Gul said Ankara would take "fresh steps" to bring about a permanent solution.
The attack occurred when a group of Turkish Cypriots went to visit a house they had owned when the island was divided in 1974.
Some reports say the group was attacked by members of a Greek Cypriot family who now occupy the house.
Two of the group received serious injuries.
Police say they have already arrested the alleged assailants.
Mr Theodorou said the incident would be "dealt with immediately, sternly and mercilessly according to the laws of the state."
"The government is determined to safeguard in every way the right of every citizen, Greek Cypriot or Turkish Cypriot, to free and safe movement," he added.
So far, as many as 50,000 Cypriots are thought to have crossed the demarcation line since it was opened last week.
But Mr Theodorou said he expected record numbers - about 40,000 - to cross on the Orthodox Easter holiday on Monday.
The island has been divided since Turkish troops invaded the north in 1974, following a brief Greek-Cypriot coup backed by the Greek Government.
Thousands of people displaced from their homes have never returned, and earlier this year a high-profile peace push by the United Nations ended in failure.
The easing of border restrictions comes a week after the Greek Cypriots signed the European Union accession treaty paving the way for EU membership next year.
But EU membership will, in effect, apply only in the internationally-recognised Greek part of Cyprus if the island is not unified in time for formal membership in May 2004.