BANGKOK — Singapore’s government has been trying for two weeks to get the Harvard economist Li Shengwu, a grandson of Singapore’s founder, Lee Kuan Yew, to apologize for comments he made in a private Facebook post that were seen as critical of the country’s leadership.

The Singapore attorney general’s office even drafted an apology letter for Mr. Li to sign, in which he would admit to contempt of court and to making what it called “false and baseless” statements.

But on Friday, Mr. Li declined to give in to the demands of the government, which is led by his uncle, Prime Minister Lee Hsien Loong, and refused to sign the apology. In the Facebook post last month, he said that some foreign news outlets engaged in self-censorship when covering the prime minister because of the threat of legal action in Singapore.

The dispute is the latest in a bitter family drama that has riveted the city-state and raised questions about the legacy of Mr. Lee, Singapore’s first prime minister, and how the nation should be governed after 58 years of one-party rule.