Former governors Anies Baswedan and Ganjar Pranowo said the resounding victory of Defence Minister Prabowo was helped by pressure on regional officials from a partisan administration and President Joko Widodo, with social aid used as a tool to ensure just one outcome.
Anies said the election showed the world's third largest democracy was at risk of sliding back towards its authoritarian past, and warned it could set a bad precedent.
"This practice will be perceived as normal, a habit," he told the Constitutional Court.
The outgoing administration of Widodo has rejected accusations of election interference.
Prabowo received nearly 60 per cent of the votes, helped by the tacit backing of hugely popular former rival Widodo.
He promised to maintain his predecessor's agenda of refurbishing infrastructure, adding jobs and developing downstream industries to better exploit Indonesia's vast mineral resources.
Anies received a quarter of the vote and the third-placed Ganjar Pranowo took 16 per cent.
Challenges to election outcomes are typical in Indonesia and the court is expected to hand down its decision on April 22.
Anies' team urged the court to disqualify Prabowo from the ballot, as a beneficiary of unfair practices, asking it to order Widodo to keep neutral in any re-run of the election, and not use the state apparatus or budget to help one candidate.
Widodo's conflicts of interest violated a constitutional provision for fair and just elections, as well as the law on corruption in state governance, his legal team said.
"Was the 2024 election held freely, honestly, and justly? Anies asked the court. "Allow us to answer: No. What happened was the opposite."
Prabowo has maintained he won clearly and fairly. Anies' presentation lacked evidence, his legal team said on Wednesday.
Ganjar's team asked the court to order an election re-run by June 26, disqualifying Prabowo and his running mate Gibran Rakabuming Raka, who is Widodo's son, saying his last-minute inclusion on the ticket had unfairly influenced the vote.
Widodo's "nepotism and abuse of power" regarding the election violated the constitution, they added, citing Gibran's candidacy and appointment of his supporters in regional roles.
"Violations in the election are surprising to us because they destroyed our morals, which is an abuse of power," Ganjar told the court.
Gibran was only able to run due to a sudden rule change by the same court where Widodo's brother-in-law, Anwar Usman, was chief justice.
Anwar has been barred from presiding over election disputes since an ethics panel found him guilty of violations.
Widodo's supporters denied that he abused his position to help Prabowo.
