An unprecedented family feud between Singapore's prime minister and his sister over the death of their father Lee Kuan Yew has burst into the open in the strictly-controlled city-state.

Lee Hsien Loong said that he is "deeply saddened" that his sister Lee Wei Ling had accused him of abusing his power to commemorate the first anniversary of their father's death in order to establish a dynasty.

"The accusations are untrue," the prime minister said of the comments by Dr Lee, a well known neurosurgeon, on her Facebook page.

The feud is a political bombshell in Singapore where the People's Action Party founded by the elder Mr Lee has remained solidly united since taking power in 1959.