The Dormant Bank and Building Society Accounts Bill received its second reading in the House of Commons last week.
The scheme will distribute assets that remain unclaimed for more than 15 years to youth and financial inclusion projects through the Big Lottery Fund. The Government maintains that it should be voluntary.
Liz Atkins, director of public policy at the NCVO, said: "We believe there must be a reserve power to enable the Government to make the scheme mandatory."
During the debate, Labour MP Tom Levitt said similar schemes in other countries were compulsory. But Yvette Cooper, Chief Secretary to the Treasury, said the banking industry intended to participate and the Government would monitor progress.
The NCVO also said the Government should hold a consultation on the causes that should benefit from dormant bank deposits. "These resources could provide essential support to meet a wide range of needs in the community," said Atkins.
Susan Kramer, third sector spokeswoman for the Liberal Democrats, said many dormant accounts contained money left to charities in wills. She called for help for charities to identify the accounts and reclaim the money.