Merkel said Kramp-Karrenbauer and Spahn plan to run for the CDU post.
She later told press that she was stepping down as party leader was the first step towards a leadership transition.
Her party's latest election setback happened Sunday in the central state of Hesse.
Merkel's conservative Christian Democrats (CDU) came home first in the election in the western state of Hesse, but polled just 27.2 percent of the vote, projections for broadcaster ZDF based on preliminary results showed.
The BBC's Jenny Hill, in Berlin, says the latest setback comes amid a bad year for the chancellor where her coalition government has lurched unhappily from crisis to crisis.
Usually, within the party, the chancellor is also the chair of the CDU, but this is not enshrined in stone.
UBS reports huge wealth generated by China, warns against trade tensions
If the existing US/China trade-war escalates, UBS foresees lower economic growth in both countries before policy responses. But Chinese billionaires expanded their wealth at almost double that pace, growing by 39 percent to $1.12 trillion.
After Angela Merkel announces she will step down as Germany's Chancellor in 2021, Eva Oer says she could not escape taking some of the blame for poor election results.
Merkel loyalists would be unlikely to vote for Spahn, who would have to compete with other Merkel critics for the remaining votes.
"This may be one reason why Merkel sticks around a bit longer", Campbell said.
Mr. Merz has courted support from the CDU Economic Council due to clear economic policy.
Merkel has been CDU chairwoman since 2000 and giving up the role would start a race within the party to succeed her as chancellor.
The end of the long love affair with the CDU no doubt began in 2015 and 2016, when Ms. Merkel welcomed a million migrants, majority Syrians, as a humanitarian gesture. Ms. Kramp-Karrenbauer, known as AKK within the CDU, led Saarland as premier for the past seven years.
Several killed in USA shooting near Pittsburgh synagogue
Reporter Myles Miller, of PIX11, noted, "For those who don't know, Squirrel Hill is Pittsburgh's largest Jewish neighborhood". In a statement , Wolf condemned the shooting, saying these "senseless acts of violence are not who we are as Americans".
But Merkel also has to shore up support among her own party, where more and more members are calling her leadership into question. A disastrous result for either or both parties could further destabilize the national government and ultimately the position of Merkel, Germany's leader for the past 13 years.
The 57-year-old minister-president of the federal state of North Rhine-Westphalia is frequently put forward as a possible Merkel replacement by his allies, even though Laschet has refrained from making such suggestions himself.
Nahles declined to comment Monday on the reports that Merkel might step down as CDU leader.
Angela Merkel's announcement has seen a flurry of predictions as to who could replace her.
Railing against the newcomers, the far-right anti-immigrant AfD is now the biggest opposition party in the Bundestag, and has seats in all of Germany's state parliaments.
Global media expressed concern that she would be distracted from major issues overseas such as Brexit and hoped she would stick around to accompany the process. Political experts see this as Merkel responding to voters after recent elections and calming the nerves within her party. She reminded listeners she had always wanted to exercise her post with dignity, and likewise, leave in a dignified manner. It took her six months to piece together a coalition which has been riven by infighting and suffered losses in regional ballots in Bavaria and, on Sunday, Hesse.
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On Friday, Defense Secretary Jim Mattis authorized the use of troops and other military resources at the U.S. -Mexico border. Migrants must also apply for refuge with the National Migration Institute. "If we go alone anything could happen", she said.
Yet the potential for change in Germany is hemmed in by the country's constitution and relatively strong political center.