The German Chancellor hit out after Mr Trump threatened to “totally destroy” North Korea as fears of a nuclear conflict mount.
Mrs Merkel said: “I am against threats of this kind. And speaking for myself and the Government I must say that we consider any type of military solution absolutely inappropriate and we are counting on diplomatic efforts.
“This must be vigorously implemented. In my opinion sanctions and enforcing these sanctions are the right answer.”
The United Nations agreed to impose new import limits on North Korea after Kim Jong-un’s regime launched two missiles over Hokkaido before crashing into the Sea of Japan.
Mrs Merkel lashed out at Mr Trump, saying that sanctions were the only solution to rein in the North Korean threat.
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She told German broadcaster Deutsche Welle: “Anything else with regard to North Korea I think is wrong. And that is why we clearly disagree with the US President.”
Mr Trump, whose speech was met with applause in New York, said the United States would not skirt away from military action if forced to react to North Korean attacks.
The US President also warned America’s other rivals would “go to hell” for their actions before issuing a rallying cry for unity.
Mr Trump said: “We must work together against those who threaten with chaos and terror.
“No-one has shown more contempt for other nations and the well-being of their people than the depraved regime of North Korea.
“They respect neither their own citizens nor the sovereign rights of countries.
“If the righteous men do not confront the wicked few then evil will triumph.”
The US is currently taking part in bombing drills alongside South Korea.
The drills are the first flights since North Korea conducted its sixth and most powerful nuclear test on September 3 – along with staging another missile test over Japan, sending regional tensions soaring.
South Korean Defence Minister Song Young-moo said drills will be conducted “two to three days a month these days” because of the growing tension with the DPRK.