Greece had argued that the young country's name implied a claim to the territory and ancient heritage of Greece's northern region of Macedonia.
"We will not divide the Greeks in order to unite the (Macedonians)". Macedonia's friendship treaty with Bulgaria has contributed to this effort since its finalisation in January 2018, with bilateral trade between the countries rising at an annualised rate of 11 percent in the following six months.
The agreement has angered hardliners and nationalists on both sides of the border who feel their countries have made too much of a concession to the other.
The deal reached by the two countries' prime ministers is expected to be signed by their foreign ministers this weekend.
"This agreement is unacceptable and I will not permit its legalisation", he said in a televised address, noting that Greece had got everything it had asked for, while Macedonia received nothing.
Ivanov's comments came a day after Zaev and Tsipras announced a compromise in the 27-year-long row over the name of the small Balkan country, saying they had agreed on the new name of the Republic of Northern Macedonia.
Greek Prime Minister Alexis Tsipras and Zoran Zaev of Macedonia agreed Tuesday to rename the latter's country North Macedonia, ending a disagreement that has prevented it from joining global institutions such as NATO.
Zaev and his Greek counterpart, Alexis Tsipras, have also faced political dissent.
The head of the All-Macedonian National Council - Makedonijum, Straso Olumcev, said they had gathered spontaneously to express revolt over what happened on Tuesday, MIA said. After that, Macedonia's parliament would vote on it, and if it is approved, Mr Ivanov's signature would be needed.
"This agreement sets an example for others on how to consolidate peace and stability across the region".
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"President Ivanov. left the meeting, refusing to talk about the achievements of this historical agreement", the government said in a statement.
In Macedonia, Zaev's government unanimously adopted the agreement, government spokesman Mile Boshnjakovski told reporters after the session.
Tuesday's agreement paves the way for Macedonia to advance in its bid to join the European Union and North Atlantic Treaty Organisation.
The deal was welcomed by European Union officials.
Romania and the Republic of Macedonia established diplomatic relations in 1992, one year after the formation of the independent state of Macedonia.
A positive breakthrough in the relations was reached previous year with the signing of a bilateral friendship pact in a region beset by ethnic and territorial disputes.
The prime ministers of Greece and Macedonia faced political storms at home Thursday, two days after reaching a historic deal to settle a decades-old dispute over Macedonia's name.
He also ruled out a Greek referendum on the name-change.
"This achieves a clear distinction between Greek Macedonia and our northern neighbors and puts an end to the irredentism which their current constitutional name implies", he said.