"First of all, we must be careful not to accept his game," Oettinger, a German, told Deutschlandfunk radio.
Trump has launched a series of withering attacks on Germany, the EU's biggest economy. He said the EU had become a "vehicle" for German interests and predicted that more member states would vote to leave the bloc as Britain did last June.
Trump has warned German car companies that he would impose a border tax of 35 percent on vehicles imported to the US market. His top trade adviser has accused Germany of using a "grossly undervalued" euro to gain advantage over the United States and its own European Union partners.
German Chancellor Angela Merkel has rejected that charge, pointing out that the European Central Bank is in charge of the euro and that Germany respected its independence.
Merkel was the go-to European ally for former US president Barack Obama, who praised her as "an outstanding partner" on a farewell visit to Berlin in November. Under Trump, the relationship has deteriorated rapidly.
Oettinger urged the EU to be self-confident in its dealings with Trump. "We have the bigger market," he said. "As a team we are stronger."
Editor: Ade P Marboen
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