JOHANNESBURG—South Africa’s Parliament erupted in chaos on Thursday, as security forces dragged from the chamber opposition politicians who interrupted President Jacob Zuma’s state-of-the-nation address with calls for him to answer long-standing corruption allegations.

Julius Malema, a former protégé of Mr. Zuma’s who entered Parliament last year as the leader of a party opposed to his rule, called for Mr. Zuma to repay a portion of more than $20 million in state funds spent renovating Mr. Zuma’s private home.

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