Aleksandar Novakovski, the electoral commission chief, said the elections were conducted in "a good atmosphere, without incidents and with no major irregularities".
"There will be a second round," he told reporters.
Ivanov, 49, of the right-wing VMRO-DPMNE party, is the clear favourite to win the second round scheduled for April 5.
While voting in Skopje, Ivanov appealed to voters of the majority Slavic Macedonian nation to "behave responsibly to contribute to... the European perspective for Macedonia".
Erwan Fouere, the EU envoy based in Skopje, said Organisation for Security and Co-operation in Europe observers would be issuing an assessment report on Sunday's poll.
"The elections took place in a calm atmosphere and we commend the members of the electoral boards and citizens of this country who despite the harsh weather came out to vote," he said.
Security was tight on Sunday with police deploying 8,500 officers to prevent any recurrence of the violence that rocked last year's parliamentary elections in the former Yugoslav republic which became independent in 1991.
|The electoral chief and observers said the polls were held in a "good atmosphere" [EPA]
On election day last June one person was killed and several others wounded in shootings in an ethnic Albanian area.
That incident raised fears that Macedonia's EU membership would be further delayed.
Four years after becoming an official candidate to join the bloc, Macedonia is yet to start EU accession talks.
And its hopes of entering the Nato military alliance have also been blocked by Greece over an 18-year name dispute.
Athens, which objects to the name Macedonia because it is also used for Greece's northernmost province, vetoed its admission to Nato in 2008.