Just four months after taking office, Merz's conservative Christian Democrats (CDU) and the centre-left Social Democrats (SPD) have been openly clashing over Merz's plans for cuts in what he says is an "unaffordable" welfare system.
SPD Vice Chancellor and Finance Minister Lars Klingbeil has instead been pushing for tax increases on top earners, an idea Merz has rejected.
Merz is expected to meet with Klingbeil and SPD co-leader and Labour Minister Baerbel Bas in the late afternoon. Markus Söder, head of the CSU, the CDU's Bavarian sister party, will also attend.
The meeting comes days after Bas raised eyebrows by describing claims that Germany's welfare system is unaffordable as "bullshit".
Merz hit back at this in an interview with Sat1 television on Tuesday, saying he had spoken to Bas and told her "this is not the sort of language I want used within the coalition".
He added that five billion euros could be saved by making cuts to benefits for the unemployed and low earners.
Over the next few weeks the coalition will have to finalise the budget for this year and sign off the one for 2026, while deciding how to plug a budget gap projected to reach 30 billion euros in 2027.
The friction between the two parties has sparked memories of the fractious three-way coalition under previous SPD chancellor Olaf Scholz, which fell apart last year after constant internal bickering over fiscal policy.
The CDU/CSU won the resulting early general election in February but was left with only the SPD as a viable coalition partner.
Merz has characterised his government as "not a love marriage but a coalition with a job to do".
The two parties have agreed on some major changes, such as amending Germany's constitution to allow massive borrowing to rebuild the armed forces and upgrade national infrastructure.
But tensions within the coalition have also caused public spats.
The most notable was in July over what should have been the routine nomination of a new judge to Germany's highest court.
The CDU/CSU withdrew support for the SPD's nominee Frauke Brosius-Gersdorf after a right-wing media campaign accused her of being a left-wing activist on issues such as abortion.
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That sparked fury in the SPD ranks, where many have also chafed against Merz's hard line on immigration and his limited enthusiasm for climate protection.
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