Greek officials predict Prime Minister Alexis Tsipras will survive a no-confidence vote in parliament later this week.
Tsipras called for the vote Monday after defense minister Panos Kammenos resigned and pulled his nationalist ANEL party from the ruling coalition.
Kammenos quit to protest the deal with neighboring Macedonia over the use of the name Macedonia.
ANEL leaving the coalition leaves Tsipras' ruling leftist Syriza Party without a majority of seats in parliament, opening the door to possible early elections.
But a government spokesman says the party is confident of winning the no-confidence vote, set for Wednesday, and completing its four-year term in October.
The U.N.-brokered deal with Macedonia ends a nearly 30 year-long dispute over who gets to use the name.
If approved by the Greek parliament, the former Yugoslav republic would be officially called the Republic of North Macedonia.
But many Greeks, especially nationalists, are still upset, saying the name should exclusively belong the ancient region of northern Greece, made famous by Alexander the Great.
They say letting the country of Macedonia use it implies territorial claims on the region.
The dispute has held up Macedonia's desires to join NATO and the European Union because of Greek objections.