The leftist duo beat Finance Minister Olaf Scholz and Klara Geywitz, who said they would support their rivals after winning just 45.33% of the votes.
Germany's junior governing party is set to announce the results of a ballot on its new leadership.
RAMALLAH - Israeli soldiers shot dead on Saturday night a Palestinian young man near the southern West Bank city of Hebron.
During the hustings, Ms Esken and Mr Walter-Borjans made clear that they are not prepared to remain in a coalition unless Ms Merkel's party give in to a series of high-stakes demands, including extra billions in spending on infrastructure and a hike in the minimum wage.
Walter-Borjans is a former finance minister of Germany's most populous state, while Esken is a federal lawmaker.
Cut off from its "social roots", the party seems "too rarely an alternative" to Merkel's CDU, he told AFP.
Walter-Borjans and Esken, who obtained a joint ticket, want to renegotiate the coalition agreement to focus more on social justice, investment and climate policies, placing them in collision with Christian Democrats (CDU) of Chancellor Angela Merkel.
The leadership race was triggered by the departure of the SPD's previous leader, Andrea Nahles, after the party's poor showing in European Parliament elections. SPD delegates will approve the leadership, chosen by a vote of the party that ended on Saturday, at a party conference that will begin on December 6.
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The NWS warned of the possibility of mud and debris flows near the burn scars of the recent Getty Fire and Palisades Fire. Friday's high in Anaheim was 57, where the forecast called for highs of 59 on Saturday , 65 on Sunday and 69 on Monday.
But she and Walter-Borjans - who unlike some contenders eliminated in the first round of voting haven't clearly advocated a fast exit - left open what exactly their position will be on the coalition's future.
Last week, Ms Kramp-Karrenbauer called for unity while threatening to stand down as CDU leader if the party failed to back her, which prompted a lengthy ovation at the annual congress.
If the SPD pull out of the shaky ruling coalition, Mrs Merkel would nearly certainly fall from power, which could mean the end of her lengthy political career.
A snap election is also in the cards. They joined the current coalition only reluctantly a year ago after Merkel was unable to put together an alternative alliance.
Ms Esken said: "We want to reach out to all, we want to reach both our hands out to all - to those who decided otherwise and supported the other team, even in the pre-election campaign".
Merkel, in power for 14 years, has said she would step down when her term ends in 2021.
Both Merkel and her SPD partners have seen their support slipping in regional elections this year.
In the latest sign that established party tie-ups are being tested, a three-way coalition consisting of CDU, SPD and the Greens agreed on Sunday on a government deal in Saxony, where the AfD came in second in a September election.