Nathan, 92, had spent 40 years in Singapore civil service and two-terms as President from 1999 to 2011. He suffered a stroke on July 31 and was in intensive care of a hospital till he passed away on August 22.
The family held a private cremation after the state funeral service.
Seven eulogies were delivered at the state funeral service led by Prime Minister Lee Hsien Loong at the National University of Singapore's University Cultural Centre this afternoon.
"He played a leadership role in the Indian community. But he was also a President for all Singaporeans, and cared deeply about racial and religious harmony," said Lee.
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A lone bugler from the military band sounded the 'Last Post' after the state funeral for the Singapore-born Nathan.
A minute of silence was also observed, after which the Rouse was sounded -- a symbolic call back to duty after respect has been paid to the memory of the deceased.
Singaporeans, led by President Tony Tan Keng Yam, and diplomats paid their last respects to the late president at the Parliament, where he was laid to rest with full honours.
Abe told Nathan's wife that Japan will never forget Nathan as he was the first head of state to visit Hiroshima and meet the atomic bomb victims during a state visit to Japan in 2009.
"For me, President Nathan was a great son of Singapore, a great educator, leader and statesman. He was also a great friend of Indonesia," wrote former Indonesian President Susilo Bambang Yudhoyono in the condolence book he signed at Singapore Embassy in Jakarta.
Ambassador-at-large Gopinath Pillai, in his tribute at the state funeral service, said giving back to the Hindu and Indian communities was of great importance to Singapore's late President.
Pillai said Nathan had told him that he took on the role of chairman of HEB because he felt that just as there were credible Indian ministers who had won the respect of all races in Singapore's political arena, the various Indian institutions here should also be credible.
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"I would venture to say that almost half the households in Singapore have a photograph of Nathan with a member of their family," Pillai said.
In that incident, two Japanese Red Army terrorists and two terrorists from the Popular Front for the Liberation of Palestine tried to blow up the Royal Dutch Shell-owned refinery Pulau (Island) Bukom.
When the terrorists' attempt failed, they hijacked a ferry boat operating between Bukom and mainland Singapore.
Nathan, then 47 and a director of Security and Intelligence Division, led negotiations and had the terrorists surrender on February 7, on condition they be flown to Kuwait and freed.
The terrorists had planned to blow up the Shell refinery and disrupt oil supply to South Vietnam to show their support for communist North Vietnam during the Vietnam war.
Nathan is survived by his wife, daughter, son and three grandchildren.
Recalling Nathan's lighter side, Pillai said he loved watching Tamil and Malayalam movies, and listening to classical Carnatic music and light film songs.
The song 'Thanjavooru Manneduthu' that played at the start of the funeral service was a favourite of his, he said.
The four women from India arrived on their motorbikes at the Causeway on the last leg of a cross-border trip across Asia to raise awareness against female feticide in India.
But officers at the Immigration and Checkpoints Authority of Singapore did not allow them to enter Singapore as they did not have proper vehicle insurance.
One of the bikers' contacts happened to know Nathan and contacted him for help.
Nathan had initiated a think-tank to develop deeper understanding between India and Singapore. He had once told the Institute of South Asian Studies (ISAS), a think-tank of National University of Singapore, to champion the understanding of a "Singapore in India and India in Singapore", Pillai said.
"While Singapore and India enjoyed friendly relations, they did not have, in his views, a deep understanding of each other. His advise to me was - you should champion a Singapore in India and India in Singapore. That way you can help increase each country's understanding of the other," he said.
He said Nathan was a man of foresight who strongly believed that diaspora of various South Asian countries had much in common.
There was much potential and value in bringing them together in neutral venue and Singapore was one of that, Pillai said, adding that Nathan was also the driving force behind the publication of Indian Diaspora book in 2006, the most comprehensive account of Indian diaspora even today.
"To show our deep gratitude for his immense contribution, the South Asian Diaspora Convention 2016, held in July, conferred on him the Outstanding Member of the South Asia Diaspora Award," Pillai added.