Gapšys has been sentenced in the party's bookkeeping fraud case.
"We must start an impeachment procedure against one of the Labour Party's leaders, Vytautas Gapšys. We are convinced that a person sentenced for bookkeeping fraud cannot be a member of the Seimas.
"Today, we are starting collecting signatures to call the session. We have consulted lawyers – the impeachment must be started, and the Constitutional Court should give its conclusion on whether a person found guilty of a crime can be a member of the Seimas," Kubilius, the leader of the conservatives political group, told a news conference on Wednesday.
The Seimas rules say that impeachment procedure should be started against an MP found guilty of criminal charges as soon as the verdict comes into force. However, the impeachment is only required for the criminal deeds he committed during his term as an MP.
In 2013, a court convicted Gapšys of fraudulent bookkeeping in the party in 2005-2006 and the Court of Appeals upheld the sentence this week.
Kubilius said "it is up to the Seimas to take the responsibility by starting an in-house probe".
"This is what we will initiate in the extraordinary session," said Kubilius.
In his words, the parliament should amend the Law on Political Parties to prevent party restructuring in cases when a party as a legal entity is suspected of corruption and is on trial.
The conservatives will propose the amendments during the extraordinary session.
Kubilius also said that the Seimas should amend the Criminal Code to clearly stipulate liability for crimes against a democratic political system.
The parliament's Vice-Speaker Gediminas Kirkilas of the Social Democrats told Žinių Radijas on Wednesday that the parliamentary Commission for Ethics and Procedures will have to have its say before deciding on whether to impeach Gapšys.
Kirkilas said the Social Democratic Party's group will vote "in the proper way" on impeachment, despite the Labour Party being their coalition partners.
Parliamentary Speaker Loreta Graužinienė, of the Labour Party, said on Monday that the court ruling did not revise the MP status and consequently did not provide grounds for an impeachment procedure, adding that Gapšys could continue his work.
According to the Seimas statute, an impeachment process is a "parliamentary procedure applied by the Seimas to the persons specified in Article 74 of the Constitution for their actions in conflict with the Constitution, carried out during the tenure of office, in order to solve the issue of the constitutional liability of such persons".