A non-governmental monitoring organisation, MOST, said Crvenkovski's centre-right opponent Sasko Kedev received around 39.4% in the election to pick a successor to Boris Trajkovski, who died in a plane crash two months ago.
MOST said it based its forecast on votes at 289 polling stations out of a total of 2973 in the Balkan country.
It also said turnout reached 53%, above a legal minimum requirement of half the electorate casting ballots.
Kedev's nationalist VMRO-DPMNE party earlier alleged fraud in the election and called on the authorities to annul it.
Crvenkovski was widely seen as the frontrunner after he came out on top in a first round of voting two weeks ago.
However, analysts would not exclude a possible surprise in the polls although Kedev, also 41, has almost no political experience. A heart surgeon by profession, he was first elected as a deputy in the Macedonian parliament in 2002.
The polls have been be monitored by about 300 international observers.