One tenth of the island's population has crossed in recent days
The Greek-Cypriot authorities have announced a series of moves to end the isolation of the Turkish half of the divided island.
As of Friday, Turkish Cypriots will be able to trade in the south, and gain access to healthcare and other state benefits available to Greek Cypriots.
The Nicosia government will also start accepting official documents - such as car registration plates - issued by the breakaway north, which is only recognised by Turkey.
The measures follow last week's decision by the Turkish Cypriot Government to relax restrictions on movement between north and south, which allowed more than 130,000 people to criss-cross the border.
The "confidence-building measures" were announced by Greek Cypriot government spokesman Kypros Chrysostomides, following a cabinet meeting on Wednesday.
I think the 2004 Olympics is a good opportunity to have Turkish Cypriots representing Cyprus
Greek Cypriot government spokesman
"The philosophy behind this is that Turkish Cypriots living in the occupied north should enjoy the same rights and benefits enjoyed by all citizens of Cyprus," Mr Chrysostomides told a news conference in Nicosia.
He said Cyprus wanted to improve education ties between north and south significantly, and to restore telephone connections between the two communities.
The spokesman also said the government sought to encourage Turkish Cypriots to play at international level for predominantly Greek Cypriot sports teams.
"I think the 2004 Olympics is a good opportunity to have Turkish Cypriots representing Cyprus," Mr Chrysostomides said.
After last week's decision by the Turkish Cypriot authorities to ease travel restrictions with the south, an estimated tenth of the divided island's population - crossed the UN-patrolled "Green Line".
Queues stretched for several kilometres, with many people having to wait for hours to cross to the other side.
Also for the first time in almost 30 years, Greek Cypriots were allowed to stay up to three nights in hotels in the north, rather than being confined to day trips.
So far, three checkpoints have been opened.
Cyprus 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 peace effort 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.