Indonesian President Joko Widodo has announced that he has won re-election after receiving an estimated 54% of the vote. His promise to wait for official results was reversed after his challenger made improbable victories.

Following a meeting with his coalition parties, Widodo told reporters that the heads of state of Malaysia, Singapore, Turkey and other countries had congratulated him on a second term.

The electoral estimate is based on so-called quick counts of a sample of polling stations by a dozen respected poll organizations. Widodo said nearly 100% of the polling stations were counted. The fast count was correct in previous elections.

"We all know that the QC [quick count] Calculation is a scientific calculation method. According to the country's past election experience, the accuracy is 99.9%, which is close to the actual count, "said Widodo.

Widodo's rival, former General Prabowo Subianto, claimed he had won 62% of the votes in Wednesday's election because he had voted for the votes of his own election campaign. He repeated a similar claim when he lost to Widodo in 2014.

The Electoral Commission must publish official results by May 22.

Indonesia, the world's most populous Muslim majority, is an outpost of democracy in a Southeast Asian neighborhood of authoritarian governments and is expected to be one of the largest economies in the world by 2030. A second term for Widodo, the first Indonesian president from outside the Jakarta elite, could further consolidate the country's two decades of democratization.

Subordinate Subianto, a strict nationalist, conducted a fear-based campaign highlighting Indonesia's weakness and the threat of failure or exploitation by foreign powers.

Widodo said he had sent a representative to speak with Subianto and his camp.

"I sent a delegate to a meeting with Prabowo this afternoon to arrange a meeting, and when people see our meeting, we will be able to show how the elections are smooth, secure and peaceful," he said ,

The country's security minister and his military and police chiefs announced on Thursday that they would suppress all attempts to disrupt public order, while tabulating the official results of presidential and parliamentary elections.

Security Secretary Wiranto, who uses a single name, told a press conference with police and military chiefs that the security forces would crack down on any "orderly" threat.

He said the 80.5% turnout gave the winner of the presidential election "high legitimacy".

National Police Chief Tito Karnavian said the election commission and the courts are the appropriate institutions to resolve complaints about the election.

Subianto's Muslim followers planned to hold mass prayers in central Jakarta on Friday, but it was not clear if the event could take place.

"I appeal to all not to mobilize, both to celebrate the victory, as well as to dissatisfaction," said Karnavian.

The election was a major logistical exercise with 193 million voters, more than 800,000 polling stations and 17 million people who opted for a smooth election process. Helicopters, boats and horses were used to bring votes to remote and inaccessible corners of the archipelago.

The voting went smoothly, except for a few districts where logistical issues led to delays, and it was peaceful, a notable achievement for a country that is marked by political violence.

The Widodo campaign highlighted its progress in reducing poverty and improving Indonesia's inadequate infrastructure with new ports, toll roads, airports and mass transit. The latter became reality last month in the chronically overcrowded Jakarta with the opening of a subway.