Widodo, the governor of Jakarta, was leading with about 52 percent of the vote, while Prabowo Subianto had about 48 percent, according to most credible quick-count surveys.
The early results are considered reliable and a good indicator of what the official count will show when all votes are tallied in about two weeks.
"At the time being, the quick counts show that Jokowi-Kalla is the winner," Widodo told a news conference, also referring to his running mate, Jusuf Kalla.
But Subianto's campaign chief, Mohammad Mahfud, said that three internal quick-count results showed their candidate was ahead. He called on supporters to remain calm as the votes continued to be counted.
A one-time furniture maker who rose from humble beginnings and is seen as a man of the people, Widodo was pitted against Subianto, a wealthy ex-army general with close links to former dictator Suharto.
The race is the third direct presidential election in Indonesia, a nation of 240 million people that has struggled with corruption and poverty.
(AP)