Speaking to Al Jazeera, Abdul Munaim Abu al-Futuh, a member of the Muslim Brotherhood group's guidance bureau, said that any military action must come in co-ordination with the government.
"We have no relations with any of those [arrested]," he said.
"We believe that any military action, even if respectful, honourable and admirable, like what the [detained men] did [by supporting the Palestinian resistance], should be carried out in co-ordination with the regime and the Egyptian state, or any other state where a military action is being carried out."
Hassan Nasrallah, Hezbollah's leader, confirmed over the weekend that the group had sent a member to Egypt who was arrested in November on charges of smuggling arms and equipment to Gaza, but denied that the group is seeking to destabilise Egypt.
Tensions between Egypt and Hezbollah have been running high since December, when Nasrallah accused Cairo of complicity with Israel in its siege of Gaza.
In a new twist to the case, the Israeli Haaretz newspaper reported on Tuesday that foreign intelligence services provided the authorities with the intelligence that contributed to the uncovering of the alleged Hezbollah cell.
Philippe Vasset, editor of Intelligence Online, told Haaretz that Mossad, the Israeli intelligence agency, and the CIA, the US intelligence agency, contributed information to Egypt that led to the uncovering of the cell.
Exchange of fire
Overnight, an exchange of fire erupted between Egyptian security forces and bedouins in central Sinai where the search is being conducted, Al Jazeera's correspondent said.
Egyptian officials said on Monday that the men were thought to have taken shelter in the town of al-Nakhl in the vast mountainous interior, where there is reportedly little security presence.
The Egyptian government has yet to provide evidence for its claims, but arrested 49 people, said to be part of the same cell, back in November.