MURIC, however, said this is not a 'U-turn' but a change of tactics in dealing with the believed misrepresentations contained in the video.
The group had threatened to take legal action against Falz if he did not take down the video. It also demanded an apology from the rapper.
MURIC had complained that the video was distasteful and that the rapper misrepresented the Chibok girls.
The video featured, among other elements, some female choreographers wearing hijab and dancing 'shaku-shaku', and a Fulani man appearing to behead an individual.
A statement issued by MURIC on Monday, June 11, said it has resolved not to take a legal action against Falz but instead took the matter to government agencies responsible for censoring films and videos.
The group said pleas from many Nigerians forced it to go soft on Falz.
"Our office has since been inundated with solidarity visits, while our telephone lines have been flooded with a deluge of calls from members, friends, well-wishers, journalists and other concerned Nigerians, majority of whom are of the Islamic faith", MURIC director, Ishaq Akintola, said in the statement.
"In deference to pleas made by well-meaning Nigerians, in order to keep faith with our avowed motto (Dialogue, Not Violence) and to further confirm that MURIC is a listening, mature and responsible organisation committed to promoting peace in Nigeria, the Think-Tank resolved to drag the artist to government agencies saddled with the responsibility of censoring films and videos.
"It is not a U-turn but a sudden change in tactics."
According to the group, the new move "will have a more enduring impact not only on Falz but the entire industry" as it will make agencies to be more responsible.
The group further said, "MURIC is no longer contemplating court action against Falz, neither are we demanding an apology from him or his management.
"The likely pecuniary gain in the event of a court validation of our claims does not interest us. We are no longer looking at Falz but at a larger picture.
"The matter will now go to those government agencies who are supposed to do their jobs in the first place. Instead of creating media tension and granting cheap popularity, this matter will now be handled by professionals who know what to do.
"In the interest of peace, law and order, we are calling on the National Film And Video Censors Board (NFVCB) to take up the matter from this moment."
MURIC also maintained that Falz's 'This is Nigeria' video is "offensive and provocative," adding that it "portrays Fulanis (and Nigerian Muslims) as killers".
The viral video has largely generated rave reviews worldwide, with American hip-hop icon Diddy escalating the reach by posting it on his Instagram page.