RAMALLAH - Israeli soldiers shot dead on Saturday night a Palestinian young man near the southern West Bank city of Hebron.
After their election Walter-Borjans and Esken promised to try to unite and strengthen the party.
Walter-Borjans is an economist served as finance minister of Germany's federal state of North Rhine-Westphalia from 2010 until 2017.
Their appointment still needs the formal approval of a party congress next week, which also is expected to consider whether the party should stay in the "grand coalition" of Germany's traditional big parties led by the center-right Merkel.
Walter-Borjans and Esken have said they want to renegotiate the coalition agreement to increase focus on issues closer to the SPD's values, including social justice.
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 are set to approve the leadership - elected via a party ballot that ended Saturday - at a party conference starting on December 6.
Rivals Norbert Walter-Borjans and Saskia Esken have sounded much more skeptical and advocated changes to the coalition agreement.
During the campaign Esken and Walter-Borjans said their price for staying includes billions of euros of government investment in climate and education, a €12 (S$18) per hour minimum wage, and wage negotiations that should be made obligatory for employers.
"We have always said this is not just about whether we leave immediately or stay in for the duration", he told Phoenix television, adding he meant to see which policies could be done with Merkel party and which could not. "We all know it, you know that today we must stand together".
Conservative lawmaker Alexander Dobrindt of the Christian Social Union (CSU), the Bavarian sister party of the CDU, also said that there was no reason to end the coalition, according to an interview with the Augsburger Allgemeine paper. "We stand by this coalition on the basis that has been negotiated".
The shock result heralded a week of uncertainty for the coalition, with next Friday a key date as the SPD is to vote on whether to stay in government when it meets for its annual congress.
Some have said a snap election or a minority government could be on the cards.
Merkel, 65, has been in power since 2005 and has said she will not seek re-election at the next national election, due in 2021. The next election is now due in the fall of 2021 but there have always been questions over whether the coalition will last until then.
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.