SEOUL—The U.S. and South Korea offered to return to negotiations with North Korea in a bid to reduce tensions that American officials said run the risk of a direct military conflict.

Senior South Korean officials, who met with Secretary of State John Kerry in Seoul on Friday, said their government also was willing to resume humanitarian assistance to the North following weeks of escalating threats by North Korean leader Kim Jong Eun to attack American and allied targets in North Asia and the Pacific.

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