"There could be an agreement between the political groups should they want to help the ruling majority in passing good decisions for Lithuania," Ramūnas Karbauskis told BNS.
"However, we couldn't invite them as a party to join the coalition because of the (influence peddling) suspicions," he added.
As part of the agreement, the Order and Justice group could be offered the post of deputy speaker in the Seimas, Karbauskis said.
According to him, the same cooperation proposal might be made to the Electoral Action of Poles in Lithuania–Christian Families Alliance (LLRA-KŠS).
The seven-member Order and Justice group has declared itself as an opposition group.
Lrt.lt was the first to report about a possible cooperation agreement between the Order and Justice and the LVŽS on Wednesday.
Rolandas Paksas, the Order and Justice Party's honorary chairman, told the website that he had met reputedly both with Karbauskis and Prime Minister Saulius Skvernelis in the past month to discuss possible cooperation.