TOKYO—SoftBank Group Corp. said it would spend as much as ¥500 billion ($4.8 billion) to buy back up to 7% of its own shares, following plunging stock prices and a pressure campaign from one of the world’s most aggressive activists.

The proposed share buyback isn’t as large as the one urged by Elliott Management Corp., which had recently built a $2.5 billion stake in the Japanese tech giant and was pushing for as much as $20 billion in share purchases, The Wall Street Journal has reported. But it is SoftBank’s second major…

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