The LSDP leader also told reporters after a meeting of the party's leadership that he will not stand as candidate for deputy Seimas speaker for a second time and that the party will propose Mindaugas Bastys for the post.
Vainiutė is not a member of any party.
Julius Pagojus, a Social Democrat, was appointed justice minister last week, but he stepped down amid criticism over last year's incident in which he was caught by the police drunk-driving.
The Social Democrats had initially proposed Darius Petrošius for justice minister, but the former parliamentarian withdrew his candidacy after his suitability for the post was publicly questioned due to his family's alleged links with Arūnas Pukelis, a controversial businessman in Tauragė, a town in western Lithuania.
The LSDP then decided to propose Julius Sabatauskas, chairman of the parliament's Committee on Legal Affairs, for justice minister, but the Peasants and Greens did not back the 58-year-old Social Democrat for the post, saying that they "want people from the new, younger generation who are not related to certain politicking" in the new coalition government.
PM-designate Skvernelis has no doubts about Vainiutė
Lithuania's Prime Minister-Designate Saulius Skvernelis so far has no doubts about professor Vainiutė.
"I have no doubts about the candidate so far," Skvernelis told BNS Lithuania on Wednesday evening.
He said he would meet with the candidate shortly, expressing hope that Vainiute is designated before the new government's program goes on discussion at the Lithuanian parliament next Tuesday.
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