Greece says it prevented around 260,000 migrants from crossing its border with Turkey in 2022.
Ankara insists it has adhered to international law, but if a migrant qualifies for refugee status they cannot be ruled to have broken the law by crossing a border.
Many of the migrants come from war-torn countries, mainly Afghanistan and Syria.
Greece has often been accused by human rights organisations of forcing some of them back into Turkey.
In October 92 men, who were mostly from Afghanistan and Syria, were found almost naked and bruised at the border.
At the time the UN refugee agency said in a tweet that it was “deeply distressed by the shocking reports."
On Saturday the minister of citizen protection showed ambassadors from other European Union countries, as well as Switzerland and the United Kingdom, a section of an expanding border wall with Turkey. He told them that it also acts as one of the European Union's borders.
"It is a message of application of international law and I believe that Turkey should receive it," Christos Stylianides said.
The five-metre-high steel wall faces east across the Evros river which marks the border.
Greece is expanding the wall, adding a 35-kilometre stretch with the ultimate goal of extending it to cover most of the 192-kilometre border.
The EU's border protection agency, Frontex will also send another 400 guards to the border, adding to the existing 1,800-strong force.
Athens has repeatedly accused Turkey of weaponising the plight of migrants, encouraging them to cross the border to put pressure on Greece and the rest of the EU and effectively cooperating with people traffickers.
Meanwhile Turkey accuses Greece of violent pushbacks that endanger the lives of migrants.
It hosts some 3.6 million registered Syrian refugees, more than any other country in the world.
EU leaders are worried that Turkish President Recep Tayyip Erdogan could encourage a mass exodus to the EU, where most of the migrants and refugees want to end up, preferably at one of the more prosperous bloc members.