He said his party's nearly 27% showing had forced Greek leaders to realize the bailout is "nonviable," and said Syriza would press as a member of the opposition for the bailout to be scrapped in its entirety.
Syriza, which campaigned against the terms of the bailout, got 71 seats.
The vote was widely seen as a referendum on whether Greece should remain tied to the euro, the currency used by 325 million people across 17 countries in Europe. The possibility of a "no" vote roiled world markets, with some analysts warning that the collapse of the euro would cost $1 trillion.
Samaras said he would build a government of "parties that believe in the nation's European orientation, that believe in the euro."
But he acknowledged that government budget cuts forced on the country by international lenders have caused suffering among Greeks.
The new government will have to make changes "in order for the Greek people to escape the torturous reality of unemployment and unbelievable difficulties that every Greek family faces today," Samaras said after meeting with the president earlier this week.
International bailouts have kept Greece from defaulting in the face of an ongoing recession and low tax revenue, but lenders have demanded hugely unpopular government budget cuts in exchange.
Some observers had predicted that efforts to renegotiate the bailout could lead to a run on Greek banks and deeper misery.
The country must identify additional budget cuts by the end of June to be considered compliant with the terms of its bailout.
German Chancellor Angela Merkel, Europe's powerful advocate for balancing budgets to build a strong basis for economic growth, had urged Greeks not to walk away from the international loan deals.
"We will stick to the agreements. That is the basis on which Europe will prosper," she said Saturday.