Syriza fell just two seats short in parliament of the 151 needed to rule on its own, without forming a coalition government.
The election results are likely to place Greece in conflict with the European Union and international creditors. Mr. Tsipras has promised to end years of tax increases and cuts in government programs. He has already gained the support of the Independent Greeks party. That could mean he could form a ruling coalition soon.
After the results were announced, Mr. Tsipras held talks with Panos Kammenos, the leader of Independent Greeks. The party has little in common with Syriza. But both oppose the international financial rescue plan for Greece.