During a phone call, the two leaders discussed their shared “view that the international community needs to increase pressure on the North Korean regime and that the UN Security Council must swiftly adopt new and harsher sanctions,” a spokesman said in a statement.
The German chancellor also spoke with South Korean President Moon Jae-in, who both agreed the international community should “quickly decide on further and stricter sanctions”.
German government spokesman Steffen Seibert said: “What’s important is to have close coordination among partners.
“The common goal is still to avoid military escalation and make a peaceful solution possible.”
However Russian President Vladimir Putin said on Tuesday that imposing tougher sanctions on North Korea over its nuclear missile programme would not change the leadership in Pyongyang, but could lead to large-scale human suffering.
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Putin, speaking after a BRICs summit in China, also warned against further ramping up military hysteria around North Korea, saying that could lead to “global catastrophe.”
North Korea confirmed it tested a hydrogen bomb on Sunday, and claimed the weapon is more than five times more powerful than the bomb detonated over Hiroshima.
The hermit state has had sanctions imposed on exports by the United Nations since last August, but the restrictions have so far failed to stop the country developing and testing its nuclear capabilities.
She said: “Indeed there are many worries, especially also regarding the Korea question and the aggression of the North Korean dictator.
“I don’t think that we can solve the conflict without the American president.
“But we have to clearly say for us there can only a peaceful diplomatic solution.”
Her comments followed Mr Trump’s ominous warning of “we’ll see” when asked if the US would retaliate.
And they came as US Defence Secretary James Mattis said North Korea will be met with a “massive military response” if Kim Jong-Un threatened America or its allies.