Macedonia’s prime minister, Zoran Zaev, has upped the ante in the battle over his country’s name, telling opposition MPs they either back him or he will call early elections.

“The process will not be frozen, we have to move forward,” the social democrat leader said on Monday. “We will know in a few days whether we can reach an agreement with the opposition to adopt the constitutional changes. The alternative is elections.”

In a referendum on Sunday, voters overwhelmingly backed an agreement to change the country’s name to North Macedonia, but turnout was unexpectedly low after opponents of the deal were urged to stay away.

Result of Macedonia's referendum is another victory for Russia | Simon Tisdall Read more

With all results in on Monday, the state electoral commission announced that voter participation stood at 36.8%, far short of the 50% needed to make the result valid, although 91.4% of ballots cast were in favour of the accord.

Emboldened by the results, Zaev issued the ultimatum as he attempted to muster support for the deal with Greece that has EU and Nato membership as its ultimate reward.

The nationalist opposition, with financial backing reputedly from Russia, had campaigned heavily for the plebiscite to be boycotted, arguing that the deal appeased Athens. Since seceding from Yugoslavia in 1991, Greece has argued that its neighbour’s name usurps its history and includes thinly veiled territorial claims over its own province of Macedonia.

Marko Trosanovski, of the Institute for Democracy thinktank, said: “No one expected such a low turnout. The success of the boycott was a surprise. While there might not have been tangible evidence of Russian intervention, the result goes along with Russian interests in the region.”

Moscow has long opposed Macedonia’s embrace by the west, with its prospective membership of Nato’s military alliance viewed as hostile encroachment of its own territory in Europe’s former communist east. Visiting Skopje before the referendum, the US defence secretary, James Mattis, accused Russia of engaging in “a malicious cyber activity” to wreck the ballot.

Despite denials, much of the disinformation campaign is believed to have been run from behind the iron-fenced windows and walls of the two-storey Russian embassy in the heart of Skopje.

In a terse statement on Monday, the Kremlin said it was carefully watching events in Macedonia. “We are observing closely and of course think that all processes should remain within the framework of the law,” said its spokesman, Dmitry Peskov.

Opponents of the agreement say the mass abstention has robbed the Zaev government of the grounds to rewrite the constitution to reflect the new name. By law the two-party coalition needs a two-thirds majority in the 120-member parliament to ratify the agreement. The US state department, echoing similar statements from Nato and the EU after the referendum, urged MPs to “rise above partisan politics”.

Branko Gerovski, a prominent political commentator, said: “The big issue now is how Zaev will get to that magic number, 80. There are some MPs in the opposition who might be motivated to back the deal. In the Balkans, crossing palms with silver has always helped stability, and here in Macedonia we know all about instability. It is vital that we join Nato for the security of this country.”

Polls have repeatedly shown high levels of support among Macedonians for accession to both the EU and Nato. “It is the one issue which has the highest consensus in the country,” said Trosanovski.

Backing for membership of the 29-member military alliance is especially strong among Albanians in Macedonia, as well as in Kosovo and Albania. “We are surprised, worried and disappointed that the low turnout even extended to [ethnic] Albanians in Macedonia,” said Berat Buzhala, editor-in-chief of Kosovo’s leading newspaper, Gazeta Express. “It is critical that as our immediate neighbour Macedonia joins Nato. If it fails it will only help Putin make trouble in Europe’s backyard.”

Macedonia’s main opposition party, VMRO, insisted the result was a clear rejection of the deal with Greece. “The people have clearly sent a message to Zaev that he has no legitimacy to push this deal,” it said. “Instead of manipulating, he should face the reality and reject this agreement, which is at the expense of the Republic of Macedonia.”

But insiders said at least three or four VRMO MPs with a business background were likely to back the deal. “Despite their personal grievances over the name issue, there are some who understand that if left out of the process the party will be completely marginalised,” said Gerovski. “People in business want to see the country in the EU because they know that way lies prosperity.”

With ethnic Albanians already in his coalition, Zaev is expected to also try to persuade MPs who represent the multi-ethnic republic’s Turkish, Roma, Serbian and Bosniak minorities to support the deal.

The Greek prime minister, Alexis Tsipras, who is up against his own cohort of nationalist opponents, including the party headed by his defence minister, Panos Kammenos, faces a general election next year.

“On both sides there is a sense now of time being the enemy,” said Gerovski. “If it goes down to the wire and elections are called, for sure the political crisis will deepen.”