Mitsotakis said that Prime Minister Alexis Tsipras did not have any "political legitimacy" to commit the country to a deal that is not approved by his junior government coalition partner, the Independent Greeks (ANEL).
FYR Macedonia and Greece call it truce on the 27 year old ongoing name dispute.
Zaev said resolving the long-standing issue would open Macedonia's access to North Atlantic Treaty Organisation and the European Union.
Skopje and Athens announced they can resolve their long and bitter dispute by agreeing on the composite name "Republic of North Macedonia" for Macedonia - a deal expected to unlock Skopje's European Union and NATO bids.
Thankfully, it sounds like Greece and Macedonia have finally reached a resolve, thanks to the new name of the Republic of North Macedonia - or "Severna Makedonija" in Macedonian.
Macedonia proclaimed its independence from Yugoslavia in 1991 but its worldwide recognition was immediately blocked by Greece because of the name.
In a televised address, Tsipras said the 140 countries which had recognized the Balkan state simply as Macedonia would now recognize it as Republic of North Macedonia.
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Many Greeks felt their northern neighbor was trying to hijack Greece's ancient cultural heritage.
However, the accord still requires ratification by the two national parliaments and a referendum in Macedonia.
Both Albania and Macedonia hope to launch full membership negotiations with the European Union.
The deal was welcomed by EU officials, with European Council president Donald Tusk tweeting his "sincere congratulations" to Mr Tsipras and Mr Zaev.
"This historic agreement is testament to many years of patient diplomacy and to the willingness of these two leaders to solve a dispute which has affected the region for too long", said Jens Stoltenberg, Secretary-General of North Atlantic Treaty Organisation. I believe in the democracy of the internet and want to keep this site and its enriching content free for everyone.
The dispute has poisoned relations between the two neighbors since Macedonia's independence from Yugoslavia in 1991.
In a statement, Nimetz congratulated the two prime ministers on reaching an agreement: "I have no doubt this agreement will lead to a period of enhanced relations between the two neighbouring countries and especially between their people". Athens say that name implies territorial claims on a northern Greek province of the same name.
On June 6, thousands of people protested in major cities across Greece against the compromise, while, four days earlier, like numbers of supporters of Macedonia's right-wing opposition VMRO-DPMNE party took to the streets of the capital, Skopje, to protest against a deal.