In a proposal made on Friday, an increase in the number of crossing points between Greek and Turkish-administered Cyprus was also suggested.
"It is our conviction that these initiatives will form the basis of fostering trust and security among Greek and Turkish Cypriots," Greek Cypriot government spokesman Kypros Chrysostomides said.
But the initial reaction from Turkish Cypriots was dismissive, while the Turkish government in Ankara was non-committal.
Turkish Cypriot Prime Minister Mehmet Ali Talat said the offer was misleading as the same result would have been achieved if the Greek Cypriots had accepted a UN power-sharing blueprint when it was offered to them in April.
"The proposals are a distraction from the real issues," Talat said.
"The proposals are
a distraction from
the real issues"
Mehmet Ali Talat,
Turkish Cypriot Prime Minister
There was a more cautious response from Turkey.
"Let's look at what they say. We will evaluate the proposal with our Turkish Cypriot friends and then we will make a decision," Foreign Minister Abdullah Gul said.
Turkish Cypriots won international praise for voting to reunify the island under a UN peace plan only to see the richer, majority Greek Cypriots reject it in a referendum.
The rejection meant only the Greek Cypriot part of the island was admitted into the European Union in May.
Cyprus's 180km ceasefire line is patrolled by 1200 United Nations peacekeepers, first deployed to quell violence between the two communities in 1964.
"The UN welcomes the announcement and remains as ever committed to facilitating all confidence building measures," a spokesman said.
Turkey has some 30,000 troops in northern Cyprus. Greek Cypriots, who control two thirds of the land and make up 80% of the one million population, have an army of 14,000.