STOCKHOLM—Swedish lawmakers formally backed an agreement Wednesday that allows the North Atlantic Treaty Organization to more easily operate on Swedish territory during training or in the event of a conflict or other crisis.

The government’s proposal to sign what is known as a host nation support agreement with NATO was backed by a broad majority of lawmakers. A move by the opposition Left Party to have the agreement sent for further review was voted down by 291-to-21. The agreement was struck with NATO in 2014, but not ratified.

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