Germany has been struggling to cope with 1.1 million asylum seekers that arrived in 2015 and Berlin has not yet given an official estimate for how many it expects this year.
"As a church we say that we need a reduction in the number of refugees," Cardinal Reinhard Marx, chairman of the German Bishops' Conference, told the Passauer Neue Presse daily.
Germany cannot "take in all the world's needy," Marx added.
The question of how to respond to the migrant crisis, he asserted, should not solely be a matter of "charity but also reason."
However, Marx also expressed concern at a rise in xenophobia in Germany amid the worst refugee crisis that Europe has known since World War II.
A recent example came when Germany's eurosceptic right-wing populist AfD party suggested last week that police "if need be" should threaten to shoot migrants seeking to enter the country.
Border police "should be able if need be to have recourse to their firearms -- as laid down by law," said party chairwoman Frauke Petry.
This type of speech is "unacceptable," said Marx, adding "Sadly there has always been a certain potential for right-wing extremism and racism in Germany."
"This ideology has evidently been further consolidated," he said, lamenting that the belittling of foreigners had "reached the upper classes."
Anti-Islamic group Pegida, which began as a movement in Germany in mid-2014 and has since spread to France and other European countries, called on members and sympathisers from across Europe to march Saturday under the anti-migrant banner of "Fortress Europe".