He referred to the controversial demand of minority ethnic Albanian parties, who have backed Zaev, that Albanian be made an official language across Macedonia.
Social Democrat leader Zaev hit back by accusing the president of launching a "coup" and leading the small Balkan country into a "deep crisis with immeasurable consequences".
Zaev had on Monday presented Ivanov with signatures showing support from 67 members of the 120-seat parliament, following weeks of negotiations after an inconclusive election in December.
Ivanov earlier said he would grant Zaev a mandate if he won enough backing.
But in a statement to reporters on Monday, the president warned that the country's "sovereignty and independence are being jeopardised" by negotiations over the platform "of a foreign state" -- apparently a reference to neighbouring Albania.
Ethnic Albanians make up about 25 percent of Macedonia's two million people, and Albanian is currently an official language in areas where they make up at least 20 percent of the population.
Albanian political groups, who emerged as kingmakers in the election, made their support for a new government conditional on nationwide official status being granted for their language.
Zaev has not made clear exactly what he agreed on the issue.
For three nights running, thousands have protested in the capital Skopje and other towns against the Albanian demand, fearing the "federalisation" and potential break-up of the country.
In December's election the conservative VMRO-DPMNE party, which has ruled Macedonia since 2006, won 51 seats -- two more than the Social Democrats -- but it failed to win enough support from other parties to form a government.
The vote was intended to end a crisis that erupted in February 2015 when a mass wiretapping scandal incited huge street demonstrations for and against the government, forcing the European Union to step in.
Both the EU and the United States have urged the quick formation of a government since Zaev won majority support.
But Ivanov called on the international community to "refrain from imposing solutions that would be against Macedonian state interests".
The president, who is an ally of VMRO-DPMNE leader and former premier Nikola Gruevski, said he had consulted legal experts and talked to Zaev before his announcement.
Ivanov sparked an outcry last year when he decided to grant pardons to dozens of people implicated in the wiretapping scandal, including Gruevski. He later revoked the decision.
Macedonia wants to join both NATO and the EU, but its membership has been blocked by Athens over a dispute about the country's name -- a northern region of Greece is also called Macedonia.
EU foreign policy chief Federica Mogherini is due in Skopje for talks on Thursday.