With 95 per cent of the votes counted, official results show incumbent Iliana Yotova attracted 34.6 per cent compared to 32 per cent for ex-caretaker prime minister Andrey Gyurov.
That's well short of the 50 per cent threshold for the largely ceremonial role in a race of 27 candidates.
Sunday's vote took on added significance after a series of drone attacks on merchant ships off Bulgaria's Black Sea coast that likely killed some two dozen international seafarers.
However, only about 22 per cent of eligible voters showed up to cast their ballot, according to polling agencies.
Turnout must be above 50 per cent of 6.6 million registered voters.
The poor showing was attributed by observers to voter apathy stemming from a general mistrust in politicians.
"I want to share a certain worry and tell Bulgarians that it is an illusion if they think we can change something in this country without (them) voting," Yotova said after polls closed.
The strikes, which sparked international condemnation and concerns about the growing reach of Russia's war on Ukraine, prompted Bulgaria's government to seek allied assistance to bolster maritime security.
Bulgaria has stopped short of directly accusing Russia of carrying out the attacks, but Prime Minister Rumen Radev said their outcome "benefits the Russian Federation".
Both leading presidential candidates condemned the strikes, but they differ over the broader war.
Yotova, is a 62-year-old journalist and former member of the European Parliament, and was vice president when she became acting president in January after Radev resigned to enter the parliamentary race.
Addressing supporters at a recent rally, Yotova said she "advocated for peace through negotiations, rather than force".
She's running as an independent but also has the official backing of Progressive Bulgaria and the Socialist Party, where her career began.
A victory for leftist Yotova would make her Bulgaria's first elected female president.
Gyurov, 50, who served as caretaker prime minister this year and is a former deputy governor of the central bank, is supported by pro-Western, reformist parties and has long expressed firm support for Ukraine.
He signed a security cooperation agreement with Kyiv during his time as premier.
"I want Bulgaria to have a voice of its own in Europe. A reliable NATO ally that defends its interests through preparedness, strong diplomacy and a clear position," he recently told supporters.
Some observers believe Gyurov could have a better chance in a runoff, where results can be influenced by voters who supported candidates eliminated in the first round.
As well as the widening hostilities in the Black Sea, the campaign has focused on growing economic hardship.
Candidates have sought to address public anxiety over rising energy prices and inflation, as many families, particularly in rural areas, struggle to make ends meet.
Presidents in Bulgaria are elected directly for a five-year term and can serve no more than two terms.
While the post is primarily ceremonial, the direct election gives the president greater political authority.
The president leads the armed forces and can veto legislation, sign international treaties and appoint ambassadors.
With AP
