CSU leader Markus Söder told public broadcaster ARD's Tagesthemen TV show that the results in Bavaria give him a clear mandate for "a strong and stable government."
He said he would hold talks with the conservative Free Voters party this week to continue the existing governing coalition.
"We will ensure that a democratic and good Bavaria is preserved even in these times," Söder told the broadcaster.
Söder, who has been critical of Germany's welcoming policy towards migrants and refugees over the past decade, said the results from his state's election as well as the election in the western state of Hesse made it clear that a new tougher migrant policy was needed.
"We perceive the AfD as a right-wing extremist party," Söder said, adding that while mainstream politics should not follow the far-right party's hardline promises on migration, a slightly tougher policy was now needed.
“Then you can significantly reduce the AfD's [surge in popularity],” he added.