MOSCOW—Belarus’s president, Alexander Lukashenko, facing growing nationwide protests, said he was ready to share power, but only on his own terms, as the main opposition leader said she was ready to lead the Eastern European country.

Demonstrators took to the streets in cities and towns around Belarus for a ninth consecutive day Monday, while some state-enterprise workers went on strike, venting their frustration over the country’s disputed Aug. 9 presidential vote.

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