Officials warned however that a second, parallel counting of the ballots still underway could see the result flip given how close the two parties were.
The Socialist party had been tipped to win the elections.
Election officials were waiting for the second count to apportion the 18 seats the country has at the European Parliament.
Biser Trajanov, spokesman for the central electoral commission, said: "The results are very close, so we will validate them and will announce the final official results and seat distribution on Tuesday or early Wednesday."
The nationalist "Attack" party won 14.22 per cent of the vote and could get between two to three seats.
The liberal party of former king Simeon Saxe-Coburg, the third coalition partner, won 6.26 per cent.
Voter turnout was just 28.6 per cent, the lowest since 1990, as more than two-thirds of eligible voters stayed at home, many disillusioned by a lack of progress in the two-year-old coalition government's reforms and fight against crime.