Outgoing president Iliana Iotova and former caretaker prime minister Andrey Gyurov will face each other in a runoff on 1 November. Exit polls by polling agencies show Iotova won about 35% and Gyurov about 32.5% in the first round on Sunday, 25 October.
The polling agency Sova Harris predicted this in early October. It said Iotova and Valchev led among people who had already decided how to vote, with Gyurov and Kandev second.
Earlier on this topic: Sova Harris: Iotova and Valchev at 50.2%, runoff with Gyurov and Kandev
The agencies estimate turnout at about 22%, the lowest since the fall of communism in 1989.
Vazrazhdane leader Kostadin Kostadinov is third with about 14%.
Vote count data, released after midnight local time, confirmed the trend in the exit polls. With nearly 18% of votes counted, Iotova has 35% and Gyurov 30%.
Pre-election polls by three agencies gave Iotova between 43% and 47% and Gyurov up to 30%, a gap of up to 17 percentage points. No one was above 50%, and turnout was expected to reach 40% at most.
A candidate who wins more than half the votes cannot be elected in the first round if fewer than 50% of eligible voters cast ballots.
Polling stations opened at 07:00 local time (05:00 GMT) and closed at 20:00 (18:00 GMT), when the first exit polls came out. Voting took place at more than 11,600 polling stations, and about 6.6m people are on the voter lists. There were 27 candidates for the post.
Iotova, 62, is a former TV journalist and former MP for the Bulgarian Socialist Party. She served as vice-president alongside Rumen Radev for almost 10 years, until January this year.
Radev then stepped down to run in the early parliamentary election in April, and Iotova became outgoing president, meaning an interim head of state. Radev won the election by a large majority with his Progressive Bulgaria party and is now prime minister.
Gyurov, 50, is an economist, a former MP and a former deputy governor of the Bulgarian National Bank. The caretaker government he led ran the country for four months this year, from February to May. Pro-European parties back him.
The two differ most clearly on Russia's war against Ukraine, which Russia began with a full-scale invasion in February 2022.
Iotova wants to restore relations with Russia, which is waging war on Ukraine, and to end military aid to Kyiv, relying on diplomacy alone. During the campaign she also said Ukraine should get help by all means, financial and humanitarian.
"The more we invest in weapons deliveries, the later the war will end. The war in Ukraine has no military solution," Iotova said during the campaign. She thus opposes aid to a country that Russia has been striking since February 2022.
Gyurov wants support for Kyiv to continue and grow. He backs the EU and NATO policy of deterring Russia, which invaded Ukraine. He believes that since Bulgaria left the Coalition of the Willing in July, it is a weak and vulnerable ally.
During the campaign, Gyurov said it is in Bulgaria's interest to take an active part in the coalition and have a voice when decisions are made on how to guarantee European security. "The outcome of the war in Ukraine will shape the security order in Europe," he said.
In Bulgaria's parliamentary republic, the president has mostly ceremonial and protocol duties, but also some political influence. The president can send laws passed by parliament back with objections, dissolve the National Assembly and hand out the mandate to form a government.
The head of state is supreme commander of the armed forces and chairs the Consultative Council for National Security.