The issue has triggered mass protests both in Skopje and Athens in previous months.
According to this agreement, Macedonia was to be renamed the Republic of Northern Macedonia.
The statements came during a debate in parliament on a no-confidence motion brought against the government by the opposition for its handling of a name deal.
Protesters in Athens were planning a demonstration outside Parliament later Saturday.
Except instead of harboring goodwill for its neighbor, Greece has a beef with Macedonia's name, alleging it implies ownership of the Greek state of Macedonia and historical ties with Macedon, the ancient Greek kingdom once helmed by Alexander the Great.
Greece and Macedonia will sign an accord on Sunday to change the name of the former Yugoslav republic, the Greek government's press ministry said on Friday as the governments of both countries faced mounting opposition at home over the deal.
In Greece, the deal only faces ratification in parliament once Macedonia has performed all of its part of the process.
The provisional accord is to be signed in the fishing village of Psarades on the Prespes Lakes by the respective foreign ministers and longterm United Nations envoy Matthew Nimetz, with Prime Ministers Alexis Tsipras and Zoran Zaev in attendance.
"This is the most forward-looking deal the country has ever had in its hands", said Interior Minister Panos Skourletis.
Tsipras and his Macedonian counterpart Zoran Zaev announced the breakthrough Tuesday, after a 27-year dispute.
In Athens, there is anger over the government's acceptance that its neighbour will be able to refer to its language and ethnicity as "Macedonian".
Across the border, Zaev has also met with opposition, with President Gjorge Ivanov saying he will not sign off on the agreement.
Few thought resolving Macedonia's name dispute would be easy.
They agreed that the former Yugoslav republic can be called the "Republic of Northern Macedonia", and in return, Greece will stop blocking Macedonia from North Atlantic Treaty Organisation and in European Union membership talks. If Ivanov refuses to sign off on the deal, it will be sent back to parliament for a second vote.
"We will not divide the Greeks in order to unite the (Macedonians)", he said.
Zaharieva expressed the hope that at its meeting on June 29 2018, the European Council would decide to start EU membership negotiations with Macedonia.
Under the agreement reached, Zaev said the name to be used both internationally and bilaterally would be the Republic of North Macedonia.
But the government suffered a loss in its parliamentary majority after lawmaker Dimitris Kammenos of the nationalist Independent Greeks, the government's junior coalition partner, voted in favor.