ATHENS — Resisting mounting pressure from Europe to quickly resolve Greece’s political crisis, the leader of a left-wing party that placed second at the polls on Sunday effectively ruled out forming a coalition with the two dominant parties, raising the prospect of new elections and increasing chances the country could default on its heavy debt load and potentially exit the euro zone.

Alexis Tsipras, the leader of the Coalition of the Radical Left, known as Syriza, was given a mandate from President Karolos Papoulias to try to form a government on Tuesday, after the front-runner, Antonis Samaras, the leader of New Democracy, failed to do so on Monday.

Yet, to the consternation of European leaders and financial markets, Mr. Tsipras held true to his party’s platform of opposing the loan agreement that Greece made with its so-called troika of foreign lenders: the European Commission, the European Central Bank and the International Monetary Fund. He called on the two dominant parties that backed the bailout, the Socialists, led by Evangelos Venizelos, and New Democracy, to revoke the deal.

He said ominously, for European leaders hoping for a quick resolution, “The popular verdict clearly renders the bailout deal null.”