In a fax sent to Aljazeera on Saturday, the group, Saraya al-Mujahidiin said they would release the hostages in response to a call from Iraq's Muslim Clerics Association.
The group also called on the Japanese people to pressure their government to withdraw its troops from Iraq.
Aljazeera on Thursday aired a tape from the group showing the hostages in capture. The group earlier threatened to burn alive Noriaki Imai, 18, Soichiro Koriyama, 32, and Nahoko Tokato, 34, if Japan did not withdraw troops from Iraq by a deadline on Sunday.
Imai graduated from high school last month. He is a member of the Campaign to Abolish Depleted Uranium and travelled to Iraq on 1 April to study the effects of depleted uranium on Iraqi children.
Koriyama is a former soldier turned freelance photojournalist.
Takato, is an aid worker and peace activist. She travelled to Iraq in April 2003, after US and British tanks entered Baghdad.
Also on Saturday, Aljazeera aired a videotape showing a US detainee kidnapped by Saraya al-Mujahidiin during an attack on a US convoy transporting supplies and fuel on the Baghdad-Falluja highway on Friday.
The captive, Thomas Hamil, is American and is working for a private company supporting the military operation.
A copy of the fax that was sent to
Aljazeera by Saraya al-Mujahidiin
He said he was the only member of the US convoy to be rescued. He also said his captors treated him well and offered him complete care.
Aljazeera also aired an audio tape from the kidnappers. "Up to now your prisoner is being dealt with in the tolerant manner specified by Islamic law. Our one request is to break the siege of the city of the mosques (in Falluja) during the 12 hours from six o'clock on Saturday evening," said the group in the tape.
"If not, he will be dealt with worse that those who were
killed and burned in Falluja," the voice added in the tape.