North Korean leader Kim Jong-Un, who has not been seen for nearly a month due to apparent health problems, sent a congratulatory message to China on its national day Wednesday, state media said.

Kim was last seen in public on September 3. A rare admission from North Korea that he was suffering "discomfort" has triggered frenzied speculation about his health and close scrutiny of any mention of the young leader in state media.

The three-paragraph message sent to Chinese President Xi Jinping marked the 65th anniversary of the founding of the People's Republic of China, the Korean Central News Agency (KCNA) reported.

Kim voiced his hopes for China's future prosperity and the happiness of the Chinese people, KCNA said.

Kim took over the reins of power in North Korea following the death of his father Kim Jong-Il in December 2011.

He sent similar national day messages to the Chinese head of state in 2012 and 2013.

Recent state TV footage of Kim had shown him looking overweight and walking with a pronounced limp, which some analysts took to be a symptom of chronic gout.

Rumours about his health multiplied after Kim failed to attend a meeting of the North's rubber-stamp parliament last week.