Said Dujarric: "The secretary-general calls on all parties to respect the results of these elections in order to help consolidate the peace process, which aims to build a secure and prosperous Aceh within a united and democratic Indonesia."
Quick counts, or statistical surveys of vote returns with a margin of error of 1 to 2 per cent, indicate that Irwandi has secured about 39 per cent of the vote.
Irwandi, who negotiated for the Free Aceh Movement separatists in talks with Jakarta, said late on Monday that he would wait for the commission's official result before declaring victory.
But the 46-year-old, more of an academic than a gun-toting rebel, said the road ahead would not be easy.
"My response is this is the dream of the Acehnese people being fulfilled and they want fundamental change in all aspects of life and governance. It will be hard work for me," he said.
In Jakarta, Jusuf Kalla, the vice-president of Indonesia, said the government would respect the outcome "whomever the winner".
But General Djoko Suyanto, Indonesia's military chief, said the preliminary was indicative of "a victory for the Acehnese people" and not a victory for the former rebels.
He added that the military would work to uphold peace.
The Helsinki peace deal ended almost three decades of conflict in the province located on the northeastern tip of Sumatra.
The government and the separatist movement signed a preliminary peace deal in July last year followed by a memorandum of understanding on issues ranging from local governance and security arrangements to human rights.