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PARIS — Secretary of State Hillary Rodham Clinton warned China on Friday that it would face economic insecurity and diplomatic isolation if it did not sign on to tough new sanctions against Iran for its nuclear program, raising the pressure on Beijing to fall in line with an American-led campaign.

Speaking to students at the École Militaire, the prestigious French war college, Mrs. Clinton said, “China will be under a lot of pressure to recognize the destabilizing effect that a nuclear-armed Iran would have in the gulf” — referring to the Persian Gulf — “from which they receive a significant percentage of their oil supplies.”

With Russia increasingly frustrated by Iran’s recalcitrance, China has emerged as the lone...