A respective constitutional amendment on Thursday passed the second reading in the parliament with 63 votes in favor, 21 against and 16 abstentions.
In the next stage, the amendment will require at least 94 votes to be passed.
A constitutional amendment must be debated and voted on twice by the Seimas, with an interval of at least three months between the votes.
The amendment, tabled by the ruling bloc, would allow an impeached person to be elected president or a member of the Seimas following ten years after his or her removal from office.
The opposition has put forward an alternative amendment that would allow an impeached person to run for parliament, but would prevent him or her from being elected as president or holding the post of the speaker of the parliament.
Paksas has been barred from running for either president or national parliament since his impeachment back in 2004.