The amendments would allow a person removed from office through impeachment to be elected as lawmaker and president, as well as appointed as minister, prime minister and judge or state ombudsman, after 10 years have passed since the impeachment vote.
The amendments have been signed by 72 lawmakers, including members of the ruling Lithuanian Farmers and Greens Union's political group in the Seimas, the Social Democratic Labour group, the Order and Justice group and several MPs of the Electoral Action of Poles in Lithuania–Christian Families Alliance.
The 72 parliamentarians also include two Liberal MPs, Jonas Varkalys and Jonas Liesys.
Two opposition parties - the Homeland Union–Lithuanian Christian Democrats and the Liberal Movement - have tabled another package of constitutional amendments that would allow Paksas to run for parliament, but would not open the way for him to run for president.
The opposition-proposed amendments earlier this week passed the first reading in the Seimas with 99 votes in favor, two against and ten abstentions.
Paksas has been barred from running for either president or parliament since his impeachment in 2004.
A constitutional amendment must be debated and voted on twice by the Seimas, with an interval of at least three months between the votes, and requires a two-thirds majority, or 94 votes, to be adopted.