The case has gripped the country and created a public uproar, putting pressure on Susilo Bambang Yudhoyono, the Indonesian president, to follow through on his promises to clean up government and the police.
Nanan Soekarna, a police spokesman, told reporters late on Tuesday: "For the sake of the larger interest and not because of any pressure, the police have decided their detention orders should be temporarily lifted.
"[Overhaul is needed] not only in the middle and lower levels, but also the top level ... because if you look at this, do you think people can trust them?"
Teten Masduki, secretary-general, Transparency International Indonesia
"But it doesn't mean they're free because freedom requires the certainty of the law. The court will determine right or wrong, not the police."
Soekarna said that one of the senior police officers at the heart of the alleged plot will be questioned by a presidential "fact-finding team".
Chandra and Bibit have denied the extortion and abuse of power allegations, saying the case was fabricated and that they were wrongfully dismissed from their jobs.
The more than four hours of tapes played out in the court increased demands for the release of men.
The KPK, which is seen as one of the few clean institutions in the country, had made the recordings as part of an investigation of Anggoro Widjojo, an Indonesian businessmen, and his brother Anggodo.
In the recordings, Anggodo discusses ways of implicating Chandra and Bibit.
"What should be out is not extortion, but bribery," he tells one person who is not identified by name. In another section, another unidentified man says: "I will kill Chandra once he's detained."
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.
|Critics say the anti-corruption agency has many enemies due to its success [AFP]
"The president should use this for a total reform of the police and the attorney-general's office," Teten Masduki, the secretary-general of Transparency International Indonesia, said.
"Not only the middle and lower levels, but also the top level."
Masduki said that a complete overhaul was necessary "because if you look at this, do you think people can trust them?".
Adnan Buyung Nasution, appointed by Yudhoyono this week to head an investigation of the police handling of the case, said the tapes had "many interesting things from the seemingly central and dominant role of Anggodo, from the police, and other names I need not mention".
"This is not a problem involving several individuals but this is a systemic problem," he told Indonesia's MetroTV.
Nasution said that his team would talk to police and officials from the attorney-general's office who were allegedly speaking or mentioned on the tapes.
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.