SYDNEY—Australia on Saturday disputed U.S. President Donald Trump’s apparent assertion the day before that the country being exempted from planned U.S. tariffs on aluminum and steel imports would be conditional on a new security agreement.

On Twitter, Mr. Trump said Friday that his Australian counterpart “is committed to having a very fair and reciprocal military and trade relationship. Working very quickly on a security agreement so we don’t have to impose steel or aluminum tariffs on our ally, the great nation of Australia!”

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