Conservative leader Merkel and Steinmeier, who is a senior member of the Social Democrats (SPD), have been at pains to stress how closely they are co-ordinating on policy since the Ukraine crisis began, despite the traditionally warmer ties to Moscow maintained by the leftist SPD.
Andreas Schockenhoff, a senior ally of Merkel in her party, on Tuesday took issue with several of Steinmeier's recent comments, for example his warning the European Union not to force eastern European countries to have to choose between East or West.
"That is a very problematic remark ... it was Russia and not the EU that forced Ukraine into such a choice," Schockenhoff told Reuters ahead of a speech he is due to give on Wednesday in which he will criticise elements of Germany's stance.
Schockenhoff, who served as co-ordinator for Russian and German civil ties in Merkel's previous centre-right government, also criticised Steinmeier for saying at last week's NATO foreign ministers meeting that he did not see Ukraine joining the alliance - noting parliament had not discussed this and it infringed on Ukraine's freedom of choice.
"Just because Russia categorically insists that Ukraine must never become a member of NATO, we shouldn't have to accommodate this," he said.
Steinmeier's view that Russia had no interest in having a collapsing state in its neighbourhood was either "a very western, 'enlightened' way of looking at things or wishful thinking," he told Reuters.
Steinmeier forged strong ties with Russia when working for SPD chancellor Gerhard Schroeder, who cultivated a macho rapport with Russian President Vladimir Putin.
Merkel said last Saturday no one should doubt Europe's willingness to introduce tougher sanctions against Russia if it takes further steps to destabilise Ukraine. Some EU countries might have differences over Ukraine, she said, but this would not get in the way of a united approach.
The EU and the United States have responded to Russia's annexation of Crimea by imposing targeted visa bans and asset freezes against Russian and Ukrainian individuals.
The German business community, which has close ties to Russia, has publicly criticised the West for taking what some executives have described as an overly confrontational approach with Russia.
Merkel's coalition is involved in a number of other internal disputes, for example over how long telecommunications companies can store citizens' data.