The Union is debating its position on migration and integration issues.
After sharp criticism of the traffic light reform plans from the ranks of the parliamentary group in the Bundestag, the Schleswig-Holstein Prime Minister Daniel Günther (CDU) has now approved.
"A lot of things are right" about the idea of a right of residence, which has been in force since January, Günther told the Tagesspiegel newspaper.
The aim is to give those who have been tolerated for many years a title so that they can meet the requirements for a right of residence.
Helen Bubrowski
Political correspondent in Berlin.
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The majority of the Union faction in the Bundestag rejected the law because it created "disincentives".
About 20 MPs abstained, including Armin Laschet.
Günther also supports the traffic light's plan to make naturalization possible after five instead of eight years.
"The CDU is well advised to see immigration as something positive," said Günther.
It's not about hiding difficulties.
"But we have to be cosmopolitan in Germany - if only to get the huge labor and skilled worker problem under control and to avert massive losses in prosperity."
You have to speak plain language, but at the same time express yourself sensitively enough so that nobody gets hurt.
"This also applies to the debate about New Year's Eve - people with a migration background felt thrown into the same pot, although the vast majority of them condemn the riots themselves."
CDU General Secretary Mario Czaja also said that the CDU had "so far not emotionally reached people with a migration background".
"We want to do that much better in the future."