They waged their campaign in Israel as the world Jewish community pressed European institutions to come clean about their past.
"We must exhaust all of the processes, according to law, in order to ensure that everything will be done to expose the remnants of inheritances and to return them to their rightful owners," Knesset member Colette Avital, who is heading the committee, said at Wednesday's session.
Galia Maor, chief executive of Bank Leumi — Israel's second largest bank, which experts say has the most Holocaust-era accounts — said the bank would be happy to cooperate.
She added that the bank has publicized a list of all accounts that were dormant since 1955, but not those that had earlier been handed over to Israel's custodian general.
Bank Hapoalim, Israel's biggest bank, said it found only 170 accounts dating back to 1944 in its files, but could not locate one-third of the holders and transferred them to the custodian as well.
There are still a number of issues to be tackled, including legal questions regarding banking secrecy and how to calculate the current value of dormant accounts.