Singaporeans stood in silence as Lee Kuan Yew's coffin travelled on a ceremonial gun carriage a short distance from the presidential palace to Parliament.
The 91-year-old died after more than a month of battling severe pneumonia. The government declared a week of mourning for the leader who is credited with transforming the resource-poor island into a wealthy finance and trade hub with low crime and corruption.
Hundreds of mourners lined the street outsides the presidential palace, where Mr Lee's remains lay at a two-day private wake, as the carriage with his coffin draped with a Singapore flag in a glass case was escorted by Singapore's prime minister and his eldest son, Lee Hsien Loong, and other children.
Mr Lee will lie in state ahead of a funeral on Sunday.
Many raised smartphones to record the procession and some were heard chanting Mr Lee's name quietly and others applauded. Roads nearby were closed despite peak-hour traffic.
Outside Parliament, people formed a long line to view Mr Lee's body, some carrying umbrellas to protect against the tropical sun.
"He has contributed all his life for the country and we respect him for what he has done. Look at Singapore now, without him, we are not here today," said Irene Kang, who came to pay her respects.
The state funeral will be at the National University of Singapore on Sunday.
Among those attending will be south-east Asian heads of state and Prime Ministers Narendra Modi of India and Tony Abbott of Australia.