Chancellor Angela Merkel has ramped up the rhetoric in a warning to migrants ahead of September's general election.
Speaking in her weekly podcast, she stressed that refugees in Germany must respect tolerance, openness and freedom of religion, while senior members of her party called for a ban on foreign funding of mosques.
Merkel, who will seek a fourth term as chancellor in what is expected to be a tight election, has come under fire for allowing more than one million refugees to enter Germany over the past two years.
She said: "We expect the people who come to us to stick to our laws."
Merkel said it was paramount that new arrivals respected and understood the liberal values of modern Germany such as tolerance, openness, freedom of religion and freedom of opinion.
The CDU leader urged Germans to show openness in return: "We know very few things about Syria, we know very few things about Iraq or African countries. And we must see this as an opportunity to learn more and experience more."
The party has lost support since her decision, in 2015, to leave Germany's borders open for hundreds of thousands of refugees fleeing the civil war in Syria and Iraq.
Immigration and security are set to be major issues in the election, in which the far-right, anti-immigrant Alternative for Germany (AfD) party is expected to enter the Bundestag.
In an attempt to address unease among traditional CDU voters over Merkel's migration policy, CDU deputy party leader Julia Klöckner called for stricter rules for Islamic preachers and a ban on foreign funding of mosques – echoing comments made by other senior CDU members in recent days.