Banks have since September imposed increasingly tight limits on dollar withdrawals and transfers abroad as part of measures to tackle a severe liquidity crisis.
But bankers stand accused of sending millions of dollars abroad despite those limitations enacted since mass anti-government protests erupted on 17 October.
Lebanese banking association head Salim Sfeir, as well as representatives from 14 banks, appeared before financial prosecutor Ali Ibrahim, the sources said.
They testified "over the transfer abroad of 2.3 billion dollars during the two months since the start of the popular uprising", they said.
They were questioned over "the causes of the transfers abroad of the money of bank owners, which reduced liquidity in the internal financial markets".
They were also asked why other depositors were unable to make transfers abroad for trade or to pay tuition fees.
Bankers were asked to justify "the inability of depositors to withdraw from their US dollar accounts... while that restriction did not apply to the powerful".
Lebanon is currently facing its worst economic crisis since its 1975-1990 civil war.
The value of the Lebanese pound has plummeted on the black market, prices have risen, and many businesses have been forced to slash salaries, dismiss staff or close.
Lebanon is one of the most indebted countries in the world, with a public debt equivalent to 150 percent of its GDP.
The country is now under pressure to pay a $1.2 billion Eurobond maturity on 9 March.
Economists warn payment on time would eat away at plummeting foreign currency reserves, while bankers say a default would damage Lebanon's reputation with lenders.
Bank of America Merill Lynch in a November report estimated that around 50 percent of Eurobonds were held by local banks, while the central bank had around 11 percent.
Foreign investors owned the remainder, or around 39 percent, it said.
But these figures may have changed, with local media reporting that local banks have recently sold a chunk of their Eurobonds to foreign lenders.
The judicial sources said those summoned on Monday were also asked about those sales, but they did not provide further details on their answers.
Representatives of other banks are to be called in later this week.
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