"All the accusations are lies and a fabrication aimed at setting the people of Egypt against Hezbollah," he said.
On Thursday, Egypt's public prosecutor ordered the accused to be kept in custody for another 15 days for further questioning.
Nasrallah said Shihab, a Lebanese citizen, was in Egypt on a "logistical mission" related to the Gaza Strip.
"What he was doing [in Egypt] was a logistical job to help Palestinians get [military] equipment.
"If helping the Palestinians is a crime ... we are proud of it"
"If helping the Palestinians is a crime, I officially admit to my crime … and if it is an accusation, we are proud of it. Everybody knows that this is not the first time Hezbollah has tried to furnish arms to the Palestinians," he said.
Rula Amin, Al Jazeera's correspondent in Beirut, said" "Hezbollah has never denied that it supports the resistance in Gaza.
"It sees it as a duty for all Arab countries to support Hamas, Islamic Jihad and other groups in Gaza in order to resist Israeli occupation. For Hezbollah, it would not be a shameful thing to smuggle money and weapons to Gaza."
Hezbollah, which is backed by Egypt's regional rivals Iran and Syria, is a staunch supporter of Hamas, the Palestinian group ruling Gaza, and has lashed out at Egypt for closing its crossing with the Palestinian enclave.
Nasrallah criticised the Egyptian government for not doing more to stop Israel's three-week offensive in Gaza, which killed more than 1,300 Palestinians before a unilateral ceasefire was declared in January.