Al-Jaish al-Islami in al-Iraq (The Islamic Army in Iraq) said this in a statement to Aljazeera on Saturday.
Indonesia said it was still trying to confirm that the captors were seeking the cleric's release in exchange for the women.
"We are in the process of confirming the alleged demands through Aljazeera," Indonesian Foreign Ministry spokesman Marty Natalegawa said.
The ministry identified the captives as Rosidah binti Anom and Rafikan binti Amin.
The captors had earlier said they had seized 10 people - two Indonesians, six Iraqis and two Lebanese - working for British electronics company G-Bell.
Indonesian President Megawati Sukarnoputri meanwhile appeared on Aljazeera on Saturday to appeal for the release of the women.
Megawati said there was no reason for the women to be held captive.
Megawati appealed to the captors
to release the Indonesian women
She said: "I ask the captors personally, and in the name of the Indonesian Republic and the government, to free the hostages and let them return peacefully to their families.
"The holy month of Ramadan is approaching and we all strive to purify our hearts and tolerate one another. I hope that my request is acceptable."
In their statement to Aljazeera the captors said the Indonesian government arrested Abu Bakr Bashir to please the Australian government.
The cleric had last month told the Indonesian Rakyat Merdeka daily in an interview that a bomb attack on the Australian embassy in Jakarta on 9 September had been part of a US and Australian conspiracy to divide Muslims.
Bashir is the focus of an ongoing
"Bashir has refused the proposal of the Islamic Army in Iraq of freeing the Indonesian captors in exchange of his release by the Indonesian government," said Aljazeera's reporter in Jakarta, Uthman al-Batiri.
"Bashir himself said that it was not acceptable that a Muslim party held Muslim women as a reason to free him.
"Bashir rejected this situation strongly and pleaded them to free the Indonesian women.
"Bashir addressed the captors to concentrate on their problems in Iraq as he did not need their help," al-Batiri said.
Bashir, who is in detention before a trial that will also focus on his alleged leadership of Jemaah Islamiyah, condemned the recent Australian embassy bombing and said the attacks could not be justified.
Bashir was cleared last year of heading the al-Qaida linked Jemaah Islamiyah, but was rearrested in April immediately after completing a sentence for other offences. Police say they have new evidence that he leads the group.