With that low a turnout, getting the required support from the Macedonian Parliament could be hard.
The people who did vote overwhelmingly backed the name change - more than 90 per cent voted yes with 63 per cent of polling stations reporting. "I expect a massive vote, a huge turnout to confirm the multiethnic nature of this country and the political unity of this country".
Near complete results on Monday showed 91.4% voted in favour, with a turnout of 36.8%.
The country's Euro-Atlantic future was "a serious matter and there should be no kidding around", Zaev said several times during his public address on Sunday night, in what was clearly a message designed for his political opponents.
Greece's refusal to recognize Macedonia as a country has barred it from participating in worldwide groups, such as NATO and the EU.Greece insists Macedonia designate itself as "North" to differentiate the country from Greece's own province of Macedonia, the birthplace of Alexander the Great. He is likely to call early elections if he fails.
Critics of the pact, including President Gjorge Ivanov, had called for Sunday's vote to be boycotted.
The West is keen to have another foothold in the Western Balkans, a region where Russian Federation, which is opposed to North Atlantic Treaty Organisation expansion, has historically had influence.
"Part of the population is concerned that the change of name will change certain identity markers, even though our nationality and language will be recognised as Macedonian", said Prof Kacarska, who gained her PhD at Leeds University.
In Athens, the Greek foreign ministry noted the "contradictory" result of the vote and said careful moves were needed to "preserve the positive potential of the deal".
The agreement faces more hurdles before it can be finalized.
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The non-binding referendum needs to be ratified in parliament by a two-thirds majority.
But Greek Prime Minister Alexis Tsipras faces problems of his own.
The June deal with Greece aims to resolve a dispute dating from Macedonia's declaration of independence from Yugoslavia in the early 1990s.
"Tzanakopoulos also referred to a climate of nationalism and distrust stoked by certain camps on both sides of the border and accused both Greece's main opposition New Democracy of gloating over the supposed political success of those in the neighboring country who insist on the name Macedonia, believe themselves to be descendants of Alexander the Great and protested in Skopje yesterday with slogans 'no to the Greek genocide'".
With most of the vote counted, only 37 per cent of eligible Macedonians had answered the question of whether to accept an agreement to change the country's name to North Macedonia in exchange for Greece's lifting of its veto on Nato and European Union membership.
Once Macedonia's Parliament has voted, the ball is in Greece's court.
Because of the dispute, Greece has vetoed Macedonia's entrance into North Atlantic Treaty Organisation and the EU. It is unclear if Tsipras will be able to muster enough votes from independent lawmakers and opposition parties to push it through.
In his own post-referendum address, the opposition VMRO DPMNE leader, Hristijan Mickoski, declared that the referendum had failed - and had exposed the wrong policies of the government. "This today is a defeat not only for the agreement with Greece, but for the crime of those who are in power". Under the country's constitution, a binding referendum would need a minimum turnout of 50 percent.
Protesters shout out slogans about boycotting the referendum on changing the country's name that would open the way for it to join North Atlantic Treaty Organisation and the European Union in Skopje, Macedonia September 30, 2018.
Pro-government media have focused on the fact that the overwhelming majority of those who did vote supported the name change. Unlike many other news organizations, we have not put up a paywall.