German Chancellor Angela Merkel's Bavarian allies slumped to their worst election results in nearly 70 years and her junior coalition partners, the center-left Social Democrats (SPD), saw support in Bavaria halved.
The preliminary results show the CSU took 37.2 percent of the vote, down about 10 points from the previous election.
If they are confirmed in the final count, it would be the party's worst performance in Bavaria, which it has dominated since 1950.
"This is a party that has come from nothing, without a real manifesto, and is suddenly the strongest party in eastern Germany today, and certain parts of which is far-right extremist", he added.
The pro-immigration and environment Greens party came in second on the ballot, taking 17.5% of the vote, while the anti-immigration far-right Alternative for Deutschland (AfD) party took 10.2% of the vote, giving it seats in the Bavarian parliament for the first time.
The CSU has governed Bavaria, the prosperous southeastern state that is home to some 13 million of Germany's 82 million people, for more than six decades.
State elections were held in Bavaria on 14 October, with both of Angela Merkel's partners in the German government - the CSU and SPD - suffering large losses.
Bavaria's State Premier Markus Soeder from the CSU also said there were "lessons to be learned from Sunday's painful results", but as the frontrunner, the party still had the right to form government.
Pointing to goings-on in Berlin, Soeder said "it's not so easy to uncouple yourself from the national trend completely".
Blume wouldn't immediately comment on the causes, but he stressed the party now has the task of forming a new government.
In Bavaria, the CSU will now try to form a coalition either with the Free Voters - its preferred option - or with the Greens who are ideologically distant. The Greens, traditionally bitter opponents, with a more liberal approach to migration and an emphasis on environmental issues, are another possibility.
The Social Democrats (SPD), also in Merkel's grand coalition, lost their second-place spot in yesterday's vote - winning just 9.9 percent - around half of what they had in the last election, according to the exit poll.
"This is a hard situation for the CSU", Interior Minister and CSU party head Horst Seehofer said Monday, acknowledging that his party would need to find a coalition partner in Bavaria.
Those opposed to Merkel's decision in 2015 to open Germany's borders to some 1mn, mainly Muslim asylum-seekers, are turning to the AfD. He almost brought down the ruling coalition in June with a demand to turn back small numbers of asylum-seekers at the German-Austrian border. That's a mini-coalition, not a grand one.
Asked if he would resign as CSU leader, Seehofer told broadcaster ZDF he was not ruling this out but there were many reasons for the party's weak result which had to be analysed.
As for the national government, "it is obvious that the whole style of our work together must change, and that hopefully was a message from this Bavarian election", Nahles said. It has not gone unnoticed that Merkel has largely been excluded from the conservative campaign in the southern German state, where the CSU is registering record lows in the polls.
The CDU's general secretary, Annegret Kramp-Karrenbauer, said the party must show "discipline" and focus on Hesse.
"AfD is trying to denigrate Islam with the same methods used by anti-Semites against Jews", she said.