Speaking on Alpha Cyprus' Alpha Kalimera programme, Letymbiotis said the most important element of Monday's announcement was the agreement for a joint meeting between the two leaders and Guterres.
He argued that the meeting demonstrates the UN Secretary-General's personal involvement in efforts to restart the Cyprus process.
According to Letymbiotis, progress achieved on confidence-building measures and methodology helped pave the way for the meeting with Guterres, while the Greek Cypriot side remains focused on achieving a substantive resumption of negotiations.
"It is not useful to argue about who proposed what"
Commenting on claims by both Christodoulides and Erhürman that the agreed proposal originated from their respective sides, Letymbiotis said it is not productive to focus on who first tabled an idea.
Instead, he argued that the emphasis should remain on the outcome.
He also referred to a proposal put forward by the Turkish Cypriot side and described as a "game changer", saying it could not be accepted because, in Nicosia's assessment, it had been formulated in coordination with Turkey.
"Kokkina was among the first proposals"
Letymbiotis said the crossing points at Kokkina and Pyroi-Athienou were among the first proposals submitted by the Greek Cypriot side.
He explained that the issue was discussed extensively during the expanded meetings in Geneva and New York but faced objections from the Turkish military.
According to the spokesman, Christodoulides also submitted alternative proposals in an effort to secure agreement on Kokkina, but without success.
"The frustration of residents and those affected in Pyrgos is entirely understandable. That is exactly why we continue to insist on both Kokkina and Pyroi-Athienou," he said.
Letymbiotis stressed that agreement on two new crossing points does not mean the Greek Cypriot side has abandoned its other requests or its efforts regarding Kokkina.
"There is still time for meaningful progress"
The spokesman said the Republic of Cyprus is already in contact with Guterres' office regarding the date and venue of the next meeting.
He also expressed the view that there remains sufficient time before the end of the UN Secretary-General's term to achieve meaningful progress on the Cyprus issue and reopen negotiations.
