The phone intercepts appeared to indicate that the case against the anti-corruption officials had been fabricated.
Susilo Bambang Yudhoyono, the president, said he had asked for their resignations, but did not call for them to be detained.
The resignations are a culmination of a month-long battle between the country's
highest anti-corruption agency and rival police and prosecutors in Indonesia, which is regularly ranked among one of the most corrupt countries in the world.
The development comes as two senior investigators in Indonesia's corruption watchdog were released six days after they were arrested on suspicion of extortion and abuse of power.
Chandra Hamzah and Bibit Samad Riyanto, the deputy chairmen of the Corruption Eradication Commission (KPK), were freed after tapped telephone recordings allegedly exposing a high-level conspiracy against the commission were played in court.
The secret recordings of police, prosecutors and the brother of a corruption suspect allegedly included discussions of ways that false charges could be brought against the two men.
|The case has angered thousands and prompted protests in the capital Jakarta [AFP]
The court proceedings were broadcast live across the country and fuelled a second day of street protests in the capital, Jakarta, in support of the KPK.
The KPK is said to have made many enemies among Indonesia's political and business elite as a result of its success in investigating and charging scores of government officials, members of parliament, business people and central bank officials.
After hearing the tapes, anti-corruption activists urged Yudhoyono to conduct a complete shake-up of the police and attorney-general's office.
Yudhoyono's new coalition government was formed last month after he won a landslide election victory on the back of promises to stamp out widespread corruption.
Wimar Witoelar, a political commentator, told Al Jazeera that the issue had developed into a full-blown political scandal.
"One could also call this a sort of cleansing out process of a corrupt system which has been in Indonesia since the days of the Suharto regime," he said.