"That talks are held is basically good for all, in particular between these two countries", Merkel said at her regular summer press conference.
Last week, Trump said Germany was wrong to allow a new $11-billion Baltic Sea pipeline to import even more Russian gas, while being slow to meet targets for North Atlantic Treaty Organisation spending.
After the inauguration, Trump wouldn't shake her hand during a photo-op in her first trip to Washington.
"Transatlantic working relationships, including with the President of the United States are of crucial value for us, and I will continue to cultivate", said Merkel.
But she also warned that Washington could no longer be relied on to deliver world order. She replied: "I'm not going to adopt that choice of words".
Asked whether she had thought about resigning, Merkel told a news conference: "No, No". "We do not always share the same opinions, but it is necessary to resolve the conflict", said Merkel.
"Yes, I believe that is the case", Merkel said in response to a question as to whether the spat between her conservative CDU and its hardline CSU sister party over whether to turn back migrants at the border had reduced her standing in the eyes of the public.
Despite trade and spending disputes between the USA and Germany, Merkel stressed the importance of maintaining a good relationship.
But she also warned that Europe has become more independent because the USA is no longer the country that guarantees order around the globe.
"On the issue of trade, we have a very serious situation in the world, I want to make that very clear", Mrs Merkel said.
After the summit Vladimir Putin and Donald trump in Helsinki, it became known that trump has made a decision to invite the Russian President to Washington in the fall of 2018 and instructed his Advisor John Bolton to address this issue.
But she added that she had been right to say a year ago that Europe could no longer depend on the United States to maintain world order.