Antonis Samaras is the fourth prime minister in eight months; he faces the daunting task of resolving Greece's economic woes.
The New Democracy party, which came in first in the election, will likely ally with the socialist party PASOK to form a government.
Greece's emerging government is expected to ask for more time to implement austerity measures. Germany is saying no. One side will have to back down.
At the core of any administration will be Antonis Samaras' New Democracy party, which came first in Sunday's vote and won 129 of Parliament's 300 seats — but not enough to govern alone.
Alex Tsipras, whose Syriza party is in a close contest for Parliament, is opposed to Greece's membership in the eurozone.
Panagiotis Pikramenos, a senior judge, will lead an interim government of 16 until elections are held.
The parties who won seats in the May 6 election could not form a coalition government, triggering new elections.