The east Mediterranean island has been divided since 1974 when Turkish troops invaded and later occupied its northern third.
Cyprus is one of the world's longest-running political crises and the talks that began in the Alpine resort of Crans-Montana last week have been billed as the best chance for a lasting solution.
The east Mediterranean island has been divided since 1974 when Turkish troops invaded and later occupied its northern third in response to an Athens-inspired putsch seeking union with Greece.
At the end of last week, UN Secretary General Antonio Guterres hailed the talks as "highly constructive" and "a historic opportunity to reach a comprehensive settlement to the conflict that has divided Cyprus for too many decades."
But on Monday the sides seemed to take a less than conciliatory line.
"The Greek position remains that ... the occupying troops must leave," Kotzias said following a morning meeting in Crans-Montana, according to a foreign ministry statement.
Turkey maintains more than 35,000 troops there, and any prospects of reunification largely hinge on a drastic reduction of Ankara's military presence.
But Turkish Deputy Prime Minister Numan Kurtulmus told media in Ankara Monday that "Turkey will not step back on the issue of security and guarantees."
"Our position on this issue will not change," he insisted.
Several previous peace drives have stumbled over the issue, with Greek Cypriots demanding a total withdrawal of what they say is an occupying force and minority Turkish-speakers fearful of ethnic violence in the event of a pullout.
A diplomatic source told AFP before the talks began that Ankara was prepared to slash its troop numbers by as much as 80 percent, but Foreign Minister Mevlut Cavusoglu flatly denied that any such withdrawal was planned.
Kotzias also lamented Monday the slow pace of the discussions, which are being headed by President Nicos Anastasiades, the Greek-Cypriot leader, and his Turkish-Cypriot counterpart Mustafa Akinci.
They are joined at the discussions by delegations from Cyprus's so-called guarantor powers of Greece, Turkey and Britain.
"We agreed on Friday to discuss two questions posed by (UN envoy Espen Barth) Eide on the security issue, ... but the (in-depth) discussions have not started. We started with procedural issues," Kotzias said.
He said there was growing pressure to call in the guarantor power prime ministers, but warned this would be "premature" since "we are in the sixth day and the (in-depth) discussions have not begun."