PARIS—French President François Hollande suspended the delivery of a powerful warship to Russia, a move that risks deepening tensions with the Kremlin over its incursions into Ukraine.

France had long threatened to delay the delivery of two Mistral-class carriers because of Moscow’s support of separatist forces in eastern Ukraine. More than a week after France missed the deadline to deliver the first of the two ships, however, Mr. Hollande on Tuesday took the formal step of indefinitely suspending the handover.

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