BERLIN (Reuters) - The German Catholic and Protestant churches warned on Tuesday against the conservative opposition's plan to crack down on immigration, which they said could break a convention against mainstream parties cooperating with the far-right.

"The timing and tone of the current debate appear deeply strange to us. It is likely to defame all migrants living in Germany, to stir up prejudices and, in our opinion, does not contribute to solving the real issues," the representatives of both churches wrote in a joint letter to parliament seen by Reuters.

Friedrich Merz, the leader of Germany's CDU/CSU conservative block which is leading polls ahead of the Feb. 23 election, is set to propose plans to restrict migration that could pass with the help of the far-right Alternative for Germany (AfD).

The anti-immigration, anti-Islam AfD is labelled as right-wing extremist by German security services but is currently polling second in nationwide surveys before the upcoming snap election in the country, where the debate on immigration intensified after a string of violent attacks by foreign-born suspects.

"The two major churches hereby point out that, according to current knowledge, the proposed changes to the law would not have prevented any of the attacks," wrote Prelate Anne Gidion, the representative of the German Protestant Churches Council (EKD) and Prelate Karl Juesten, the head of the Commissariat of German Bishops.

The churches stressed that the CDU/CSU is risking breaking a taboo on cooperation with the far-right for the first time in German post-war history.

"We fear that German democracy will suffer massive damage if this political promise is abandoned," they wrote.

The CDU, or the Christian Democratic Union, and its Bavarian sister party Christian Social Union (CSU), often commonly related as the "Union", were founded shortly after World War Two, and represent an "honest reflection of Christian and Western values", according to the CDU's website.

According to the latest church statistics from the Interior Ministry, about half of the German population belongs to Christian churches, with the Catholic and Protestant denominations represented in nearly equal proportions.

(Reporting by Andreas Rinke; Writing by Andrey Sychev; Editing by Stephen Coates)