(Updates with AfD comment paragraph 5, quotes and colour from protest in paragraph 11 onwards)

BERLIN/FRANKFURT, Jan 20 (Reuters) - Siemens Energy supervisory board chairman Joe Kaeser has warned of a resurgence of right-wing extremism in Germany, as the country enters a second week of nationwide protests against the Alternative for Germany (AfD) party.

"If everything is true as reported, then that is absolutely disgusting," said Kaeser, also chairman of the supervisory board of Daimler Truck, in an interview with Reuters published on Saturday, in reference to reports of a meeting of right-wing extremists in Potsdam.

At the meeting, migration policy including mass deportations of people of foreign origin were discussed, as reported by investigative news website Correctiv. "This triggers bitter memories," said Kaeser.

The AfD, which is polling second in nationwide surveys, has denied the plans are party policy. Co-leader Alice Weidel parted ways with one of her advisers who participated in the talks.

The AfD declined to comment on Kaeser's interview or on nationwide demonstrations against the party.

Kaeser's comments come after leaders of German companies including chip manufacturer Infineon and chemicals maker Evonik voiced their concerns earlier this week.

Highlighting lessons from Germany history, Kaeser warned of the damage to Germany's image in the world and called on German business to publicly warn of the consequences. He said he would take part in demonstrations against right-wing extremism that are taking place in many cities.

"We must not repeat this mistake. I am really worried about our democracy," he said. Speaking of understanding, tolerance and respect as the basis for free basic order in German society, he added: "Anyone who votes for the AfD is choosing to lose the prosperity of our country and its citizens."

Anti-AfD protests across Germany have gained momentum with tens of thousands gathering on the streets of Cologne, Hamburg and Berlin. In Hamburg on Friday, the turnout was so big that organisers decided to end the demo earlier for security reasons.

Further protests are planned this weekend in cities including Frankfurt and Munich. In sub-zero temperatures, tens of thousands gathered peacefully in Frankfurt's centre on Saturday, according to local police.

"It's a signal to the world that we won't let this happen without commenting on it," said protestor Steffi Kirschenmann, a social counsellor based in Frankfurt.

Lord Mayor of Frankfurt Mike Josef addressed crowds on Roemer square, the same spot where the Nazi regime had burnt books in the previous century, he reminded protesters.

Participant Ulrike Hartmann said: "we need to raise awareness among our fellow citizens that something is going wrong."

"I am grateful that tens of thousands of people are taking to the streets across Germany these days against racism, hate speech and in favour of our liberal democracy," German Chancellor Olaf Scholz said on social media platform X on Wednesday. (Reporting by Andreas Rinke and Emma-Victoria Farr; Editing by David Holmes)