The three were kidnapped last week by a group who threatened to kill them unless the Japanese government withdraws its troops from Iraq.
In a videotape aired on Aljazeera, the released hostages, who appeared unharmed, were shown sitting in the office of the AMS.
An AMS spokesperson said the organisation had "called upon everybody to do their best in order to secure the release of the hostages" and that they did not "negotiate or mediate directly".
"We further call on Arabs and Muslims to prevent any more bloodshed in Falluja", added Abd al-Salam al-Kubaisi, a leading member of the organisation.
He said the AMS hoped the released hostages would return to Falluja to witness the tragedy that had occurred there and report on it. More than 600 people have been killed since the US ambush on the town began more than a week ago.
One of the freed captives is a freelance journalist, Soichiro Koriyama, 32. The other two are Noriaki Imai, 18, who wanted to look into the effects of depleted uranium weapons and aid worker Nahoko Takato, 34.
Their families had clung to hopes that their loved ones would be released, even though the killing of an Italian captive on Wednesday raised new fears for their safety.
A Japanese foreign ministry official confirmed that three hostages had been freed and were safe.
The three were released into the
care of AMS officials
Japan, like Italy, has been a staunch supporter of the United States in Iraq and both have resolved to stand firm.
But the worsening security situation in Iraq has fuelled calls in Japan to withdraw its troops, whose activities are limited by Japanese law to "non-combat zones".
Japanese Prime Minister Junichiro Koizumi has repeatedly said he will not pull out the 550 Japanese soldiers engaged in a reconstruction mission in Samawa, southern Iraq, despite the threats.
Iranian diplomat killed
Earlier on Thursday, a senior Iranian diplomat was shot dead close to Tehran's diplomatic mission in Baghdad, Iraqi police and diplomatic staff said.
According to Aljazeera's correspondent, the slain man has been identified as Khalil Naimi, the first secretary of Iran's embassy.
The Iranian diplomat was gunned
down while driving in his car
Witnesses said a white vehicle was seen chasing the diplomat's car. Unidentified gunmen fired at the diplomat's vehicle. Naimi was hit by three bullets to the head and another three in the shoulder. The assailants fled the scene.
The correspondent reports that there is speculation the assassination may be linked to the Iranian role in the mediation between Shia leader Muqtada al-Sadr and US-led occupation forces. Further speculation is that the incident is a random killing.
However, the correspondent adds, diplomats vehicles are distinguished by their particular registration plates.
Investigations into the incident, are underway.