Ms. Kramp-Karrenbauer, 56, has followed a traditional path among Christian Democrats, rising through the party ranks to win three state election campaigns on the way to a seven-year run as governor of Saarland. This year, she left regional politics for a stint as party general secretary in Berlin, a move Ms. Merkel had encouraged.

But Ms. Kramp-Karrenbauer’s association with the chancellor may prove to be her biggest liability. She has been seeking to distance herself from Ms. Merkel recently, and on Thursday she called for increased domestic security and for a “rejuvenation” of conservative values.

She also emphasized her history of winning difficult races in Saarland, Germany’s smallest state, on the border with France. “At the end of the day, what matters is whether you can win elections and in all honesty, I have made it through a lot of elections, against a lot of opposition,” she told the public broadcaster ZDF last week. “You can be rhetorically very gifted, but at the end of the day, you need something to show for it.”

That remark was clearly a jab aimed at Mr. Merz, 62, a charismatic speaker who is remembered for his approachability during a brief term as conservative floor leader that ended when Ms. Merkel ousted him in 2002.

On Thursday, he laid out a five-point plan to attract more voters to the party, including winning back the roughly one million voters lost to the far-right party Alternative for Germany, or AfD, in the 2017 general election.

“Those are not nationalists or anti-Semites, those are voters who are disappointed with the conservatives,” Mr. Merz said in an interview with the newspaper Bild that was published online on Wednesday. “In the short term, we won’t get rid of the AfD, but we can halve it.”