"Accepting the "Macedonian language" and the "Macedonian ethnicity" constitutes a non-acceptable national concession", he said in a video posted on his official Twitter account.
A man holds a Greek flag next to a statue of Alexander the Great.
Following the latest round of discussions, Macedonia is now set to be known as the Republic of Northern Macedonia.
"There is no way back", Macedonian Prime Minister Zoran Zaev said in a press conference, Reuters reports, after he spoke with his Greek counterpart Alexis Tsipras.
But Greeks seem cool to any deal involving the continued use of the name "Macedonia" by their northern neighbour. The move is part of a plan to resolve longstanding tensions between the country and its neighbor to the south, Greece.More news: Assad Denies Moscow Dictates in Syria
"We have a deal".
Greek Prime Minister Alexis Tsipras was briefing President Prokopis Pavlopoulos on Tuesday afternoon.
European Union and North Atlantic Treaty Organisation officials have welcomed a deal between Greece and Macedonia resolving a decades-long dispute over the Balkan country's name.
In a decades-old dispute, Greece wants the former Yugoslav republic to change or modify its name to avoid any claim to the territory and ancient heritage of Greece's region of Macedonia - birthplace of ancient warrior king Alexander the Great.
The statements from diplomats trumpeting today's deal reflect the linguistic awkwardness of the issue.
This year there have been several protests against an agreement in Skopje, as well as in Athens and Greece's second city of Thessaloniki in the north.More news: Few Storm Chances For Monday
NATO Secretary General Jens Stoltenberg said Tuesday's "historic agreement" was "testament to many years of patient diplomacy", and called on the two countries' prime ministers to finalize the deal.
"We are proud that this historic agreement was reached while two progressive governments are running both of the countries", PES president Sergei Stanishev said. This will set Skopje on its path to North Atlantic Treaty Organisation membership.
"We must now make good use of the window of opportunity that has been pushed wide open to accompany and consolidate the winds of peace and cooperation in the entire region". Greece considers Macedonia a non-negotiable part of its history. Macedonia's flag is emblazoned with the Sun of Vergina - a symbol associated with the dynasty of Alexander and his father Philip.
The row between Athens and Skopje has been ongoing since 1991, when Macedonia seceded from Yugoslavia and declared its independence.
Athens and Skopje had been racing to agree the outline of a settlement before an European Union summit in late June, though any accord would need to clear a referendum in Macedonia and win approval from politicians in both countries. He has been a representative of the United Nations secretary general on the same issue since 1999.More news: Atlético agree deal to sign Thomas Lemar from Monaco