Interior Vice-Minister Gintaras Steponas Vyšniauskas told BNS on Thursday that the Gavėnas should assume responsibility for the scandal.
"We believe it would be an honorable move, as he carries personal responsibility and he is directly responsible for the situation. In our opinion, he must resign," the vice-minister said.
Nevertheless, Gavėnas notified the ministry about his plans to continue in the post.
Earlier this week, law-enforcement institutions announced that several high-ranking Migration Department officials were suspected of taking bribes in exchange for faster issuing of residence permits to foreigners.
Prosecutors say a corruption network within the Migration Department may have issued residence permits to about 100 foreigners, with the number to be specified after an investigation.
