Political analysts said the outcome greatly complicated the tiny ex-Yugoslav republic's push to join Western structures.
"Instead of having a clearer picture the outcome of the referendum will only deepen the political crisis,' said Petar Arsovski a political analyst. "We are likely heading towards early elections and Macedonia does not have time for that."
Greece and the EU tried to put a brave face on the setback.
"We hope that Mr. Zaev's initiative for a constitutional reform will be successful," Greek government spokesman Dimitris Tzanakopoulos said on Monday.
"The Greek government will continue with sobriety and prudence ... to support the need for an implementation of the deal. This opportunity must not be wasted," he said.
Greece has insisted on the change because it views the name 'Macedonia' as implying a territorial claim on a northern Greek region of that name. Greece's parliament must also approve the June name deal and, like Zaev, leftist Greek Prime Minister Alexis Tsipras also faces opposition from his nationalist foes.
An early election could be called in Macedonia for the end of November at the earliest, pushing the constitutional changes into the spring.
"The biggest risk is that this drags on and the EU’s electoral calendar overtakes things," an EU official said, referring to next May's elections to the European Parliament.
EU foreign policy chief Federica Mogherini and EU Enlargement Commissioner Johannes Hahn said in a joint statement: "The (Macedonia) parliament will now be called upon to proceed with the next steps for implementation of the name agreement by deciding on adoption" of the legal changes.
A NATO diplomat was more circumspect, saying the alliance did not want to be drawn into Macedonian domestic politics.
"But we have made it very clear that should the country turn its back on this opportunity, we don’t expect it to arise again for a very long time," he said.
In Moscow, which regards NATO enlargement as a threat to its own security, Kremlin spokesman Dmitry Peskov said: "We are observing closely and of course think that all the processes should remain within the framework of the law.