The group has failed to collect the 50,000 voter signatures required for a bill drafted by them to be debated in parliament.
"They admit that they have not collected the signatures. They have asked for permission to return the signature collection sheets on Monday," Zenonas Vaigauskas, chairman of the country's Central Electoral Commission, told BNS.
The initiators said that they had collected around 36,000 signatures.
The 12-strong group, registered by the Central Electoral Commission in mid-June, had two months to collect 50,000 signatures of registered voters to force the Seimas to vote on certain amendments to the Law on Banks.
The initiators wanted an article putting the Deposit and Investment Insurance Fund's claims second in line for payment to be removed from the law. The state-owned fund has paid nearly 4 billion litas (EUR 1.16b) to creditors who held state-insured deposits at Snoras.
The Lithuanian government nationalized Snoras last November after it was discovered that billions of litas of assets were missing from the bank. A court opened bankruptcy proceedings against the bank in December.