The mosque committee welcomed the decision, saying the petition was "very immature".
Hindu petitioners demanding carbon dating to determine the age of a purported 'Shivling' found in Varanasi's Gyanvapi mosque complex have said they will approach the country's top court against the city's senior most judge's rejection of their appeal.
"The court said that any kind of survey in the Wazookhana would be a violation of the order of the Supreme Court. We will go to the Supreme Court against the order of the Varanasi Court," Sudhir Tripathi, the lawyer representing the petitioners, told NDTV.
He added that "many" of their applications are before the court.
The next date of the hearing is October 17, when the court will decide how the hearing of the case will proceed.
Meanwhile, the mosque committee welcomed the decision, saying the petition was "very immature".
"If we are given a chance, we will prove that this is a fountain," Rais Ahmed Ansari, who represented the mosque committee, said.
The 'Shivling' or relic of Lord Shiva was found earlier this year during a video survey carried out in the Gyanvapi mosque complex on the orders of a lower court in response to a petition by five Hindu women requesting year-long access to pray at a shrine inside the mosque complex. That case is still being heard.
A Varanasi court said any survey like a carbon dating will be a violation of a Supreme Court order sealing the spot of the "Shivling" inside the mosque. Also, any harm to the structure will violate Supreme Court orders to protect the "Shivling", the court said.
Last month, four of the five Hindu petitioners had requested a scientific investigation, including carbon dating, to establish the age of the "Shivling". The women claim that ancient idols of Hindu gods and goddesses are located inside the mosque.