Only 36.9 percent of the country's 1.8 million eligible voters cast ballots in the referendum as election officials continued to tally results on October 1.
Parliamentary speaker Talat Xhaferi, an ethnic Albanian who supports the agreement, said he was unable to vote.
SKOPJE, MACEDONIA-Macedonia's government prepared for a political battle Monday to push through a deal with Greece that would ultimately pave the way for North Atlantic Treaty Organisation membership, after the agreement won overwhelming support in a referendum but with low voter turnout. This issue is bigger than anything else, bigger than party interests.
Prime Minister Zoran Zaev threatened to call early elections if parliament did not support the proposal, made non-binding by the poor turnout.
That means it could interpret the outcome as a fair reflection of public opinion regardless of how many voters participated.
The European Union's enlargement commissioner, Johannes Hahn, and the bloc's foreign-policy chief, Federica Mogherini, said in a statement that "an overwhelming majority of those who exercised their right to vote said yes", to the agreement and their European path. The name change would requires a two-thirds majority in parliament. It is for all political and institutional actors now to act within their constitutional responsibilities beyond party political lines.
The European Union has invested a considerable amount of political capital in favour of the deal and may be tempted to do what it has done in the past, which is to ignore it or ask people to vote again.
The deal would "contribute to regional stability, security, and prosperity", it added, among concerns that if people in the Western Balkans lost hope in European Union enlargement prospects, it could open up a hornet's nest of old hostilities - just two decades after the last Balkan wars.
Opponents to the name change had called for a boycott of the vote and celebrated in the street outside Parliament when turnout figures were announced, chanting slogans and waving flags.
Given the success of efforts to suppress turnout, analysts say Zaev faces a hard to muster enough support in parliament to push his agenda through.More news: Nafta: US and Canada reach new trade deal
In both Greece and Macedonia, nationalists have mounted fierce opposition to the deal, among them Macedonian President Gjorge Ivanov, who dubbed it a "flagrant violation of sovereignty".
"Many more obstacles to overcome", Bieber added in a message on Twitter.
The opposition said the low turnout proved Macedonians had rejected the name change.
"The fact is that the "name" agreement did not get a green light but a stop [sign] from the people", he told his supporters after the polls closed. Macedonia said the deal is off.
The ministry said: "The climate of nationalism and suspicion, daily fake news and extreme fanaticism unfortunately do not allow a sober assessment of the great benefits of the agreement".
Supporters of the deal, led by Mr Zaev, have focused on the vote being the lynchpin of the country's future prosperity, the key to its ability to join North Atlantic Treaty Organisation and, eventually, the EU.
Ninety percent of those who voted were in favour of the change, aimed at ending a dispute with Greece, which has its own region called Macedonia. Greece, whose northern region is also called Macedonia, sees the country's name as a political and territorial threat.
The dispute is perhaps best illustrated by the hundreds of statues and monuments highlighting the glories of ancient Macedonia, a product of an extraordinarily kitschy building spree in Skopje that was led by then-Prime Minister Nikola Gruevski, before he was arrested and tried on graft and wiretapping charges.
Zaev says North Atlantic Treaty Organisation membership will bring much needed investment in the country with unemployment rate of more than 20 percent. In 2018, the two countries settled the dispute and Macedonia is now known as The Republic of Nothern Macedonia.