Turkish voters were choosing a new president on Sunday in an election that has proved to be the greatest political challenge yet for the incumbent, Recep Tayyip Erdogan, during his 20 years as Turkey’s leading politician. After leading in the first round, he is battling the opposition leader Kemal Kilicdaroglu in a runoff.

Neither candidate surpassed the 50 percent of votes needed for an outright win in the first round of the election, on May 14, prompting Sunday’s vote.

In the time since, they have campaigned fiercely. Mr. Erdogan, 69, has held multiple events per day to characterize his rival as weak and incompetent. Mr. Kilicdaroglu, 74, has worked to increase turnout by younger voters and to court ultranationalists by taking a harder line on refugees, vowing to deport millions of them in the next year.

Mr. Erdogan has led Turkey since 2003, when he became prime minister. Initially, he was widely hailed as an Islamist democrat who promised to make the predominantly Muslim country and NATO member a bridge between the Muslim world and the West. More recently, critics have accused him of pushing Turkey toward one-man rule and exacerbating a cost-of-living crisis.