Ms. Kramp-Karrenbauer, until last week the governor of Saarland, a small western state, said she would return the spotlight to the party, known as the C.D.U., over individual members. Recalling her “favorite moment” of the Winter Olympics, she praised the German hockey team that upset the mighty Canadians to win the country’s first medal in the sport since 1976.
“It wasn’t a group of individual stars, the team was the star, and that is what matters,” she told delegates. “The star is the C.D.U. It’s not about who in the C.D.U. shines, it is about the party shining.”
Ms. Kramp-Karrenbauer urged members to focus less on what it means to be “conservative” — a frequent topic of debate — and more on how to address Germans’ fears of a globalized, digitized future.
“We want to give answers, not only as a government and a parliamentary faction, but as a party,” she said, praising even critics of the party’s leadership for spurring debates that she said were integral to setting the party path for the coming decade.
Ms. Kramp-Karrenbauer became one of several new faces at the center of power in Berlin. Ms. Merkel, 63, who remains the party’s chairwoman, on Sunday named some of its younger leaders to take on minister posts, including Jens Spahn, 37, one of her fiercest critics on migration, and Julia Klöckner, 45; both are conservative lawmakers seen as possible future chancellors.
But Ms. Kramp-Karrenbauer has been the chancellor’s favorite. She easily won re-election as governor in March, helping galvanize her party six months before a federal election.
The question of Ms. Merkel’s succession has become a pressing matter five months after inconclusive elections left the chancellor struggling to build a new government. The rapid rise of the Alternative for Germany party, fueled in part by the refugee issue, has made it harder for her to form a governing coalition.
In Saarland, Ms. Kramp-Karrenbauer has experience leading coalitions with various parties, from the free-market Free Democrats to the Social Democrats. Her policies and life story offer a mix of views with appeal both to voters who like the more modern image Ms. Merkel has given the party, and to those who hark back to its more socially conservative, Christian roots.
A Roman Catholic who married at 22, she is the main breadwinner in her family; her husband stopped working to help raise their three sons.
Even after the chancellor softened her resistance to same-sex marriage, Ms. Kramp-Karrenbauer voiced opposition to such unions.
“Many party members are bemoaning the loss of a more conservative position in the party, and she could be in a position to win back such voters who say the Christian Democrats have become too liberal,” said Marc Debus, a professor of political science at the University of Mannheim.
Weakened by her party’s poorest electoral showing since World War II, Ms. Merkel failed in her first attempt to form a coalition, with the Liberal Party and the Greens. That left her with no choice but to cobble together an agreement with her old partners, the Social Democrats, themselves badly wounded in the election.
The governing deal Ms. Merkel announced three weeks ago, now subject to the approval of the Social Democratic grass roots, did not go down well with her party. Three powerful ministries and other concessions went to the Social Democrats.
“We might as well give them the chancellery, too,” complained one conservative lawmaker.
As general secretary, one of Ms. Kramp-Karrenbauer’s first jobs will be to restore calm and discipline in a party split between those who want to move to the right and those who favor Ms. Merkel’s centrist course. She will also be asked to draw up a new party program, setting the tone for the Christian Democrats for years to come.
Ms. Kramp-Karrenbauer, whose unwieldy name is routinely shortened to A.K.K. in the German news media, caught the chancellor’s eye in 2013 during a previous round of coalition talks, and not only for her negotiating skills. Unlike others who spent breaks scheming and gossiping, she would reportedly pull up a chair, put up her feet and read.
Ms. Merkel has called herself a longtime “admirer” of Ms. Kramp-Karrenbauer. But political analysts argue that seeing her simply as a younger, West-German version of the chancellor, who hails from the former East Germany, sells short a woman admired for her own political acumen.
Ms. Kramp-Karrenbauer had supported Ms. Merkel’s decision to open the border in 2015, but adopted a tougher stance in handling the roughly 7,000 refugees who arrived in her state, drawing national attention.
She had unaccompanied minors arriving without documents undergo medical screenings to help determine their age, and lobbied for Berlin to deport anyone whose application for asylum had been rejected. Male Muslim refugees who refused to accept food from female volunteers should go hungry, she said.
Her positions reflected the views of her state’s one million inhabitants, said Daniel Kirch, chief political correspondent for the Saarbrücker Zeitung, who has followed her political career.
“She is very attuned to the moods of the people,” he said. “She reads shifts in public opinion very quickly.”
Ms. Kramp-Karrenbauer entered politics in 2000 as her state’s — and the country’s — first female interior minister, then moved on to the Education and Labor Ministries, before her election as governor, in 2011. Frustrated with her coalition partners, the Free Democrats, she called a snap election that she won, and formed a government with the Social Democrats.
In Berlin, she has allies in the conservative women’s union and in Catholic labor organizations, but lacks the extensive network she relied on to govern successfully in Saarland. Analysts say taking a leadership position in the party instead of a ministry will give her the opportunity to build a power base — even if she resisted the idea of moving onto the national political stage for years.
Her rootedness is what many supporters appreciate. The daughter of a teacher, Ms. Kramp-Karrenbauer stood on a stage in her home state during carnival last year, dressed as a cleaning lady.
“I just came back from Berlin, where I was given a shift to clean up,” she told the audience in a thick local accent.
The joke drew big laughs, and it proved prescient.
Because of an editing error, an earlier version of a caption accompanying this article gave the wrong year for a photograph of Annegret Kramp-Karrenbauer dressed as a cleaning lady. It was taken in February 2017, not this month.