"We simply must become stronger together in nuclear deterrence in Europe," Merz, expected to become Germany's next chancellor after his conservatives won last month's elections, said in an interview with Deutschlandfunk radio.
Discussions should also involve Britain -- western Europe's only other nuclear power -- Merz said.
"The changed global security situation now necessitates that we Europeans discuss this matter together," he said.
French President Emmanuel Macron announced on Wednesday that he would open a debate on extending France's nuclear deterrent to other European nations, following a call from Merz on the subject.
It came after Merz said last month he wanted a discussion on "nuclear sharing" with Paris and London.
The moves come after Trump began his second stint in the White House by reversing US policy on Ukraine and risking a historic rupture with Europe.
In Sunday's interview, Merz stressed however that any discussions in Europe would take place with a view to "complementing the American nuclear umbrella, which we of course want to maintain".
He also made it clear that "Germany will not be able, or allowed, to possess nuclear weapons itself".
Germany cannot acquire its own nuclear weapons without violating an international treaty on non-proliferation (NPT) of which it is a signatory.
With Trump pivoting away from the United States's European allies, some in Germany, including politicians from the far-right AfD party, have called for the country to acquire its own nuclear weapons.
The developments spurred Merz, whose CDU/CSU bloc are in negotiations to form a coalition with the centre-left SPD, to announce last week plans to invest massive sums in defence.
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