"I believe that we really have a chance to prevent their taking effect if we're prepared to recognise what's important, together in Germany and in the USA," Altmaier told ARD public television.
"Fighting until the last minute is worth it."
The close confidant of Chancellor Angela Merkel reported a "very positive impression" of US Secretary of Commerce Wilbur Ross, who he met earlier this week in Washington trip for last-minute talks.
"We both know what the problem is," Altmaier said, while acknowledging that any final decision on exemptions would be taken in the White House.
Developed-nation producers argue they are not responsible for the global flood of cheap metals that has undermined prices and cost jobs, pointing the finger instead at China.
Trump has promised to spare both Canada and Mexico - the US' closest trade partners and fellow signatories of the North American Free Trade Agreement (NAFTA) - from his 10-percent levy on aluminium and 25-percent tariff on steel.
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Meanwhile the European Union - which handles trade talks for Germany and 27 other member states - is pushing hard to be exempt, along with other historic US allies like Japan.
But high-ranking EU figures like European Commission President Jean-Claude Juncker have warned the bloc could impose tariffs of its own on American products if the levies go ahead.
Europeans could match "stupid with stupid," Juncker said as he announced the measures.
Trump has dismissed the promised retaliation, saying he in turn would increase border taxes on cars.
