Ampon Tangnoppakul, 62, who was dubbed "Uncle SMS", died Tuesday inside Bangkok prison hospital, while serving a 20-year sentence for sending text messages deemed insulting to the monarchy in 2010.
His death prompted renewed calls for reform of Thailand's lese majeste law, with the prime minister's supporters -- known as Red Shirts -- leading the clamour for change.
"I want to reaffirm that my government policy is to stay put," Yingluck said in response to questions about possible reform of the law.
"I have already told groups who push for amendment that the government's urgent mission is to solve economic problems," she said.
Under article 112 of the Thai criminal code, anyone convicted of insulting the king, queen, heir or regent faces up to 15 years in prison on each count.
Ampon, who was described as a "prisoner of conscience" by Amnesty International, pleaded not guilty during his trial, one in a series under the royal defamation legislation, which critics say is used to stifle free speech.
His conviction triggered rare public protests against the lese majeste law in the capital Bangkok in December.
The royal family is a highly sensitive subject in the politically turbulent kingdom. King Bhumibol Adulyadej, 84, has reigned for 66 years but has been in hospital since September 2009.