Kozakou-Marcoullis said her country was "concerned" about the situation in Syria where a brutal uprising since March 2011 has already killed at least 15,800 people, according to human rights activists.
"We have taken the position from the very beginning that we should try to avoid at all costs a military intervention. For us, military operation in Syria will mean an explosive situation in the region that will not be contained only to Syria."
The Cypriot foreign minister recalled the role Cyprus played in evacuating 65,000 foreign nationals from Lebanon in 2006 during the Lebanon-Israel summer war that year.
She said she also reminded her European counterparts about the geographical location of Cyprus, making it a destination for Syrian refugees and asylum seekers in general.
"We keep telling them, I keep telling them. In every Foreign Affairs Council (meeting) I keep reminding about the geographical proximity but also about the dangers and the threats," said Kozakou-Marcoullis.
"If these potential refugees and asylum seekers do not come by boat and sea, they will come through the occupied areas and this is our biggest problem right now with asylum seekers."
Since 1974 Turkey has occupied the northern third of Cyprus which is separated from the Republic of Cyprus by a "green line" monitored by the United Nations.
The breakaway Turkish Republic of Northern Cyprus is recognised only by Ankara.
"Imagine there is a major upheaval in the Middle East, definitely part of them will try to come this way," the minister said.
"It happened with recent uprisings in North Africa, with Italy, with Malta, and this is why one of the inherited priorities of the presidency is the conclusion of this very important European common asylum system," she added.
Kozakou-Marcoullis said northern EU countries should share the cost of receiving refugees driven from their homes by the Arab Spring uprisings with their southern counterparts, who are already bearing the brunt of the migration.
She said Cyprus would not return Syrian refugees in the near term.
"We have taken the decision recently not to send back to Syria any of the asylum seekers or illegal immigrants who are here until the situation is more clear. But there is a limit to what we can do. We are a small country," she said.
The minister also discussed with AFP the issue of the island's division, saying it will not be influenced by the fact that Cyprus will hold the six-month EU presidency.
"Not only it has never been on the agenda and it is not up to us as the presidency to bring it on the agenda," she said.
But relations with Turkey are regularly discussed at meetings of EU foreign ministers and heads of the governments, she added.
"We have always wanted dialogue with Turkey. The problem is that Turkey has built a block, a concrete block, and not only they do not recognise us but they don't even want to talk to us. So there is a complete deadlock as far as any dialogue with Turkey itself is concerned."
Ankara has decided to freeze contacts with the EU presidency while it is held by Cyprus.