LANY, Czech Republic—Russian President Vladimir Putin could be a key ally in the fight against Islamist extremists, the Czech Republic’s outspoken President Milos Zeman said, even as his stance on Moscow appeared at odds with his countrymen.

Though his post is largely ceremonial, Mr. Zeman has courted controversy with some of his views, clashing with the U.S. ambassador and canceling plans to attend a Moscow military parade under pressure from fellow Czech politicians.

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