“This expression or threat, as you will, does exist,” Annegret Kramp-Karrenbauer told a news conference during a visit to London after a report in the Washington Post newspaper.
The US daily said that Trump made the threat if Britain, France and Germany did not formally accuse Tehran of flouting the 2015 nuclear deal.
China, the United States and Russia were also signatories to the agreement but Trump in 2018 unilaterally pulled the United States out and reimposed tough sanctions on Tehran.
Tehran responded by restarting aspects of its nuclear programme that the deal had sought to limit.
London, Paris and Berlin on Tuesday announced they had triggered a dispute mechanism under the agreement in an effort to force Tehran to abide once more by its terms.
But Iran's Foreign Minister Mohammad Javad Zarif accused the trio on
Twitter of having “sold out remnants of #JCPOA (the nuclear deal) to avoid new Trump tariffs”.