Losing candidate Prabowo Subianto filed complaints to the court last month, alleging that "structural, systematic and massive fraud" by the Election Commission had destroyed his chances of leading Southeast Asia's largest economy.
In its July 22 announcement, the commission declared Mr Widodo, widely known as Jokowi, as the winner with 53% - or more than 8 million more votes - over Mr Subianto, a former general under long-time dictator Suharto.
Mr Subianto's representatives walked out before the final tally was completed. However, the candidate did not concede and called on supporters to reject the Election Commission's results, saying they were flawed and violated the principles of democracy.
Lawyer Makdir Ismail told the court Wednesday that millions of votes cast across the archipelago were invalid due to irregularities at more than 55,000 polling stations in eight provinces, including Jakarta, East Java, Papua Barat and all 14 districts in Papua. He alleged that poll officials inflated Mr Widodo's results, voters used improper registration cards and recounts were performed inconsistently.
The court will resume its hearings on Friday. The final ruling, which cannot be appealed, is expected Aug. 21.
Mr Subianto's initial court documents show their own count putting him narrowly ahead with more than 67 million votes, or 50.25%, while Mr Widodo got nearly 66.5 million, or 49.74% - even though the total does not add up to 100 percent. It questioned the validity of 2.7 million votes.
"We feel very, very hurt by irregular, dishonest and unjust practices that have been shown by the election organizers,'' Mr Subianto told the court, saying the process in Indonesia, where polling stations can report candidates receiving no votes, was worse than in totalitarian states.
"Even in North Korea, they make it 97.8%,'' he said. "But 100 percent of votes for a candidate can occur here."
Several hundred supporters of Mr Subianto's gathered outside the court building, located near the presidential palace in central Jakarta. More than 1,500 policemen were deployed to safeguard the court as well as its nine judges.
The July 9 race was Indonesia's third direct presidential election after emerging from three decades of dictatorship under Suharto, who was once Mr Subianto's father-in-law.