The All India Muslim Personal Law Board (AIMPLB) said it saw "some positive movement" in the Ayodhya land case after the Supreme Court verdict Thursday in a related matter.
It said the verdict indicated that the hearing in the case will not be done on the basis of faith.
Earlier in the day, the top court had declined to refer to a five-judge constitution bench the issue of reconsideration of its 1994 observation that the mosque is not integral to Islam.
Senior AIMPLB member Zafaryab Jilani said, "We honour the court order and see some positive movement regarding the Ayodhya case."
Another AIMPLB member Khalid Rashid Farangi Mahali said, "We respect the court verdict."
Mr Mahali said the AIMPLB had wanted the Supreme Court's 1994 observation that the mosque is not integral to Islam be put before a constitution bench "so that the matter is resolved permanently."
"Two positive things have come from this verdict," he added. "First, the Ayodhya matter will not be heard on the basis of faith and will be heard as a title suit," he told PTI.
Second, he said, the 1994 observation by court "will not make an impact" on the case.
"We hope that the final hearing of Ayodhya will be completed soon. The Ayodhya hearing should not be linked with the elections," he said, referring to next year's Lok Sabha polls.
The issue whether the mosque is integral to Islam had cropped up when a three-judge bench headed by Chief Justice Dipak Misra was hearing a batch of appeals filed against the Allahabad High Court's 2010 verdict.
In that judgment, the high court had ordered that the disputed Ram Janmabhoomi-Babri Masjid area should be divided among three parties -- the Sunni Waqf Board, the Nirmohi Akhara and Ram Lalla.