Most “quick counts” after the July 9 election placed Joko Widodo, the popular Jakarta governor, in the lead.
However, his rival Prabowo Subianto, a former general under dictator Suharto, said other polls showed he had won.
The Election Commission has since been tallying votes. Outgoing President Susilo Bambang Yudhoyono has urged both parties to respect the result.
Security will be tight for the announcement, with more than 250,000 police officers on duty across the nation.
There are fears the result could trigger violence between rival groups of supporters.
Both candidates have raised concerns about voting irregularities during the past two weeks, as ballots from nearly 500,000 polling stations have been tallied.
Reliable polls point to a win for Joko Widodo, also known as Jokowi, by about five percentage points.
Official results from the sub-district and provincial levels that have been released so far also indicate Joko Widodo has won by between three and five percentage points.
But Prabowo Subianto’s camp have said they will not accept official results until allegations of cheating are probed.
Prabowo Subianto told reporters on Sunday that if the Election Commission did not investigate possible voting fraud, that was a “crime” that “very much calls into question the legitimacy of the whole process”.
He called on the Election Commission to delay announcing the result – a request the commission rejected.
The outgoing leader, Susilo Bambang Yudhoyono, has called for calm, urging all Indonesians “to safeguard the final chapter of the election process”.
“It is important to value our unity, brotherhood and togetherness. When a nation is divided, to reunite is not easy,” he said at a meeting on Sunday with both candidates.
On Monday Susilo Bambang Yudhoyono – whose party backs Prabowo Subianto – also appeared to suggest that he should accept the results, saying: “Conceding defeat is noble.”
Candidates have two weeks to appeal to the constitutional court following the announcement of official results.
About 130 million votes were cast on July 9 following an intense election campaign.
The race has been seen as a contest between new and old-style politics. Joko Widodo draws his support from the grass-roots and is unconnected to the traditional elite.
Prabowo Subianto, meanwhile, is the son-in-law of Suharto and has faced multiple questions over alleged human rights abuses under his regime.
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