BERLIN (Reuters) - German Vice Chancellor Sigmar Gabriel compared members of the anti-immigrant Alternative for Germany (AfD) party to the Nazis in comments published on Sunday, and said some of them wanted to take German society back to the 1960s.

Speaking to the Funke Media Group, Gabriel said the AfD, which has caused outrage in the political mainstream with a string of remarks about immigrants and Muslims over the past few months, was trying to provoke a reaction.

"Everything that they are saying, I've already heard - just to be clear - from my own father, who was a Nazi to his last breath," Gabriel told the group, which owns the Berliner Morgenpost and the Hamburger Abendblatt papers among others.

Support for the AfD has risen amid deepening public unease over Chancellor Angela Merkel's open-door policy for refugees, which brought some 1.1 million migrants to Germany last year. The party is now represented in eight of 18 regional state assemblies, and has about 15 percent support in national opinion polls.

Last month, AfD Vice Chair Alexander Gauland caused a storm when he said people in Germany would not want to have national soccer star Jerome Boateng, born in Berlin to a Ghanaian father, as their neighbor.

AfD leader Frauke Petry apologized to Boateng, but herself caused controversy earlier this year when she suggested police be given powers to use firearms against illegal immigrants.

Gabriel said some AfD members opposed modern Germany's cosmopolitan and liberal values.

"They want to go back to the repressed old West German republic of the 1960s, when women were still at home and foreigners, gays and lesbians had to be invisible, and where old army songs were sung over a beer in the evening," he said.

The AfD has said the influx of mainly Muslims fleeing conflicts in Syria, Iraq and Afghanistan makes the "Islamisation of Germany" a real threat.

In May, the party backed a manifesto pledge that says Islam is not compatible with the German constitution and calls for a ban on minarets and the burqa.

(Reporting by Caroline Copley; Editing by Kevin Liffey)