Rumen Radev, candidate of the opposition Socialists, won 25.7 per cent of the votes in yesterday's election, ahead of Borisov's candidate Tsetska Tsacheva on 22.0 per cent, according to results based on over 95 percent of votes counted.
Tsacheva's poor performance is an embarrassing setback for the centre-right Borisov, 57, the burly former police chief who has been premier since late 2014.
Before yesterday's vote, Borisov had pledged to resign and call early elections if parliament speaker Tsacheva failed to beat Radev in the first round.
New elections would mean fresh turmoil in the EU's poorest nation -- the average monthly salary is 480 euros (USD 535) -- and further delay efforts to lift living standards and tackle rampant corruption.
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Analysts say that Borisov's GERB party would likely again emerge as the largest in parliament but a highly fragmented legislature would make forming a government difficult.
The job of Bulgarian president is largely ceremonial but he or she -- Tsacheva would be the first woman in the post -- is still a respected figure with some powers.
He has called for EU sanctions imposed on Russia over Ukraine to be lifted. "We have lost a lot by declaring Russia more or less an enemy," the MiG ace said in a recent radio interview.
But saying he was a "NATO general trained in the United States", Radev told reporters on Monday that he has "never put in doubt the country's Euro-Atlantic direction".
Tsacheva today called on young and middle-class voters not to support Radev, dubbing him "the red general", and telling reporters that "Bulgaria's future is at stake".