By Anshuman Daga and Marius Zaharia

SINGAPORE (Reuters) - Singapore Prime Minister Lee Hsien Loong took ill while delivering a National Day rally speech on Sunday but returned to the stage after about an hour's break.

His official Twitter account said he felt "unsteady" because of prolonged standing, heat and dehydration. "His heart is fine and he did not have a stroke," it said.

Television footage showed Lee, 64, physically shaken and holding onto the stand for support.

"I gave everybody a scare," Lee said after he returned to the stage at 10.40 pm (1440 GMT). "I will have a full check-up after this."

Lee, the eldest son of the city-state's founding father Lee Kuan Yew, was speaking about the idea that a person from any race can become President in Singapore when he took ill. When he came back, he spoke about the need to prepare for his own successor.

"Nothing that has happened has changed my timetable or my resolve to press on with a succession," Lee said. "In the next GE (general election), we will reinforce the team again and soon after the next GE, my successor must be ready to take over from me."

The ruling People's Action Party has ruled Singapore since independence in 1965, and won a decisive victory in last year's general election. The next election is due by January 2021.

One person mentioned in local media as a potential successor, Singapore Finance Minister Heng Swee Keat, suffered a stroke earlier this year but is expected to resume his duties.

Lee mentioned Heng upon his return to the stage on Sunday and said Lawrence Wong will be appointed second minister to help Heng.

"Progressively, he will come back to work," Lee said.

Deputy Prime Minister Tharman Shanmugaratnam, also seen by some observers as a potential successor, will no longer have to stand in for Heng, Lee said.

Lee rose through the ranks in the military before following in his father's footsteps into politics in 1984. He was first a member of parliament, then minister for trade and industry, finance minister and deputy prime minister. He has led the country since 2004.

Lee has twice survived cancer. He was diagnosed with lymphoma in 1992 but the cancer went into remission after successful chemotherapy. He had his prostate gland removed in February 2015.

(Reporting by Anshuman Daga and Marius Zaharia; Editing by Bill Tarrant.)