Trump during the call wished her well in the formation the government for the fourth time, the White House officials said.
He underscored the deep ties that bind the two nations, their joint efforts to promote peace and prosperity, and US commitment to their longstanding, strong alliance with the German government and its people.
Among other things, they discussed how to counter Iran's 'malign' activities in the Middle East.
Trump has been criticising Iran and the landmark 2015 nuclear deal negotiated by his predecessor, Barack Obama in conjunction with other world powers.
The agreement curtailed Tehran's nuclear ambitions in exchange for lifting punishing Western sanctions. Trump has called the deal "an embarrassment."
Trump and Merkel also addressed the nuclear deal and Iran's missile programme, and its non-compliance with the UN.
Trump has until October 16 to certify to Congress that Iran is complying. Then Congress would have 60 days to decide whether to reimpose sanctions on Tehran.
They also affirmed the importance of achieving the peaceful denuclearisation of the Korean Peninsula, the White House said.
Trump had called her before the elections to wish her. Over the weekend, Merkel, 63, won her fourth consecutive election.
The win solidifies her position as the defacto leader of Europe. Before joining politics, she was a scientist in East Germany. She has a PhD in quantum chemistry.
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