Andrius Palionis, the group's head, did not name the candidates, but said that none of them is a member of the group and that two of them are lawyers and one is a politician who has in the pasts served as deputy minister.
Palionis said that they expect to discuss the candidatures with Prime Minister Saulius Skvernelis later in the day.
Skvernelis has said that he does not rule out choosing candidates other than those proposed by the group, which was established by lawmakers who left the Lithuanian Social Democratic Party (LSDP) after it decided to pull out from the government coalition with the Lithuanian Farmers and Greens Union.
Vainiūtė handed her resignation on Tuesday, a day after President Dalia Grybauskaitė that the justice minister was not coping with her duties.
Ministers in Lithuania are appointed and dismissed by the president on the prime minister's recommendation.