The comments about the bank's governor, Riad Salameh, by Hezbollah deputy leader Sheikh Naim Qassem followed an attack on Salameh last week by Prime Minister Hassan Diab which prompted warnings from the speaker of parliament not to remove him.
The pound has slumped since October as Lebanon has sunk deeper into a financial crisis. Over the past week the currency has fallen at a rapid clip, triggering small protests and riots directed at banks that threaten broader unrest.
Qassem said the crisis pointed to a "negative performance" by the bank and said Salameh was responsible for the currency crash "but not on his own" in comments cited by broadcaster al-Jadeed.
Qassem said the "appropriate decision" must be taken to put the "country's interest ahead of all else" without further specifying.
To halt the pound's slide on a parallel market that is the primary source of hard currency amid a severe shortage, the central bank capped the selling price of dollars at 3,200 for exchange dealers.
Some dealers were selling small quantities of dollars at 4,200 pounds on Tuesday, according to one importer. A second importer said he was unable to buy any dollars. One currency dealer cited a buying price of 4,000 pounds.
Several dealers were arrested on Monday for violating the cap and a syndicate representing them said exchange bureaus would shut until they were released and the situation was resolved.
The official rate remains pegged at 1507.5 pounds to the dollar at banks, but the price remains available only for vital imports - wheat, fuel, and medicine.
Economy minister Raoul Nehme said consumer goods in the import-dependent country had risen in price by 50% since October, roughly in line with the pound's drop on the parallel market.
Diab last week blamed the longstanding governor for the currency's crash and broader financial fallout. Influential parliament speaker Nabih Berri then warned of the danger of removing him.