"The German chancellor has once in a while to dare to get into conflict with the American president. So far she has always stayed in the abstract," Schulz, of the opposition center-left Social Democrats, told Welt am Sonntag newspaper.
"You can occasionally answer a president with a clear no. I would say to Trump: 'Your reasoning over a military build-up, which isn't justified by anything, is not ours," he added.
Schulz is challenging Chancellor Angela Merkel in Germany's upcoming federal election in September. The early enthusiasm for his candidacy has faded, with his party now trailing Merkel's conservatives by double digits in opinion polls.
Schulz also said in the Sunday interview that his criticism was aimed "not only at Mrs. Merkel," but other leaders who will be attending the upcoming G20 Summit in Hamburg later this week.
"The G20 Summit will be a summit of non-binding declarations. The democratic governments should ask themselves whether they want to sign minimal consensus papers with autocrats. Instead, they should clearly distinguish themselves in climate protection, in migration and development policy," he said.
"Do we have to make concessions to Trump, to Erdogan, to Putin? No," Schulz said, referring to Turkish President Recep Tayyip Erdogan and Russian President Vladimir Putin.
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