BANGKOK — As antigovernment protesters continued their occupation of crucial parts of Bangkok’s main commercial and business districts, Prime Minister Yingluck Shinawatra on Tuesday said she was “protecting democracy” and would not resign.

“Democracy belongs to the entire Thai people,” she said in a Twitter message, a day after the leaders of the protests began what they called a shutdown of Bangkok. Although Ms. Yingluck’s party is despised by many southerners and members of the Thai elite, it remains very popular in the northern half of the country and is widely expected to win scheduled elections.

The leader of the protests, Suthep Thaugsuban, who has been charged by the authorities with rebellion, threatened on Tuesday to “close all government offices” if Ms. Yingluck did not step down in the coming days.

“And if she remains stubborn, we will take custody of the prime minister and all ministers,” he said to a cheering crowd at a major Bangkok intersection blocked by protesters. Mr. Suthep advised government ministers to “send their wives and children to somewhere so that they can escape when the emergency takes place.”