Shares in the banks soared Monday after the European Commission, the EU executive, cleared the move.
President Rosen Plevneliev, who convened party leaders at an emergency meeting on Sunday, said "there is no banking crisis but a crisis in confidence and criminal attacks."
"We have sufficient reserves, means and tools to deal with any attempt at destabilization, and we stand behind each bank that becomes the target of an attack," he said.
On Friday, First Investment Bank, the country's third-largest bank, was hit by a run, just days after the fourth-largest lender, Corpbank, had been put under special central bank supervision after itself suffering a run.
Some Bulgarians continued to withdraw money from First Investment Bank on Monday. But the queues were visibly smaller than on Friday, when the bank had to close early because of the rush to withdraw deposits.
On Monday, the Bulgarian central bank proposed changing the penal code to give prison sentences of five to ten years to those who willfully disseminate misleading information about banks. Currently, the act is only punishable with fines.
The EU Commission, the 28-nation bloc's executive whose approval of bank rescue programs is needed, said "the Bulgarian banking system is well capitalized."
Plevneliev said the country's currency will continue to remain pegged against the euro despite the volatility in the financial system.
In 1997, Bulgaria's currency, the lev, was pegged at a fixed rate to the euro under a currency board arrangement, which imposed strict financial rules aimed at restoring fiscal discipline, preventing deficit spending and controlling inflation.
Bulgaria, the European Union's poorest member country, has maintained financial stability since the 1996-1997 financial crisis that led to hyperinflation and the collapse most of the country's commercial banks.