SOFIA, Bulgaria — Prime Minister Boiko Borisov of Bulgaria announced his resignation after exit polls showed his party losing badly in Sunday’s runoff presidential election.

Surveys by several polling organizations showed General Rumen Radev, 53, a former nonpartisan chief of the Bulgarian Air Force, taking about 58 percent of the vote.

Tsetska Tsacheva, a 58-year-old lawyer and member of Borisov’s center-right party, had about 36 percent.

In the first round of voting, Radev surprisingly finished first with 25 percent of the vote, followed by Tsacheva with 22 percent.

Bulgaria, which joined the European Union a decade ago, remains the poorest member of the 28-nation bloc.

Bulgaria belongs to NATO and the EU, but many Bulgarians still feel a cultural and historical affinity with Russia, and the country’s heavily dependence on Russian energy supplies leaves it vulnerable to political pressure by the Kremlin.

A political rookie, Radev has attracted many Bulgarians who are fed up with corrupt politicians. The former NATO fighter pilot who once studied at the US Air War College in Alabama, has pledged to maintain Bulgaria’s place in NATO but also says ‘‘being pro-European does not mean being anti-Russian.’’