Representing the government and the people of India, Mukherjee, one of the few foreign speakers to give their eulogies at the Memorial Service for the anti-apartheid icon, said "we stand by you in your hour of bereavement and we share your sense of loss today".
Accompanied by a high-level delegation including UPA chairperson Sonia Gandhi and Leader of Opposition Sushma Swaraj, the President flew in early Tuesday morning to join South Africa in paying homage to Madiba, as Mandela was affectionately called.
The FNB stadium, where Mandela had made his last public appearance a few years ago, reverberated to a standing ovation when Mukherjee made his entry and his name was called out.
For India, Mukherjee said, the passing away of Mandela represents the departure of the venerated elder, a great soul.
"We pray for his eternal peace. Madiba lived a life of sacrifice and privation as he pursued a seemingly impossible goal for his people - and the world is richer for his legacy.
"We, in India, have long admired him - and all that he stood for - and we will always cherish his friendship and love for our people," he said.
The President described Mandela as a visionary who epitomised and an uncommon humaneness that inspired all of mankind.
"We have no doubt that the world will honour the historic legacy of Madiba, one of the most influential personalities of our century, who taught the world the true meaning of forgiveness and reconciliation - and steered South Africans onto the path of building a truly Rainbow Nation," he said.
Earlier, US President Barack Obama had called Mandela as a "giant of history" who earned his place in posterity through struggle, shrewdness and by showing the power of political action.
Calling the South African leader the last great liberator of the 20th century, Obama painted Mandela as a testament to how people can reach for change by fighting for their ideals and employing reason and argument to match personal sacrifice.
"It is hard to eulogize any man ... how much harder to do so for a giant of history, who moved a nation towards justice," Obama said, after being introduced to wild cheers from a rain-sodden crowd in a Soweto stadium during Mandela's memorial service.
"He was not a bust made of marble, he was a man of flesh and blood," Obama said of the man whose example inspired his own entry into politics as a student.
"Nothing he achieved was inevitable. In the arc of his life, we see a man who earned his place in history through struggle and shrewdness, persistence and faith.
"He showed us the power of action, of taking risks on behalf of our ideals," Obama said after being introduced to wild cheers from a rain-sodden crowd in a Soweto stadium during Mandela's memorial service.
Tens of thousands of South Africans united in proud, noisy celebration Tuesday at a rain-soaked emotional memorial service to global freedom icon Nelson Mandela, attended by presidents and princes and watched by millions around the world.
Songs of praise and revolution, many harking back to the apartheid era that Mandela helped condemn to history, echoed around the giant stadium in Soweto where close to 100 world leaders had come to pay tribute to a man whose life story earned uncommon universal respect. The event began at midday (1000 GMT) with a stirring rendition of the national anthem, Nkosi Sikelel' iAfrika (God Bless Africa), led by a mass choir and picked up with enthusiasm by the rest of the stadium.
Some 80,000 had been expected, but the venue was two-thirds full as the ceremony got underway under a curtain of rain that had been falling since the early morning. Despite the profound sense of national sorrow triggered by Mandela's death last Thursday, the mood was upbeat, with people determined to celebrate the memory of one of the 20th century's towering political figures.
"His long walk is over, he can finally rest," African National Congress (ANC) Vice President Cyril Ramaphosa said in an opening address. In his tribute, UN Secretary General Ban Ki-moon noted that Mandela had managed to unite people in death, much as he had in life.
"Look around this stage ... we see leaders representing many points of view ... all here, all united," he said.
Crowds had begun gathering before daybreak and, as the gates opened, they swarmed into the stadium, where Mandela made his last major public appearance at the 2010 World Cup final. Wrapped in the South African flag or yellow-green coloured shawls printed with the slogan "Mandela Forever," they danced and sang -- oblivious to the constant drizzle.
"He's god given, he's god taken. We will never stop to cherish him," said Shahim Ismail, who took a day off from the sports academy he runs in Johannesburg to attend the event.
"This is once in your life. This is history," said Noma Kova, 36. "I didn't want to watch this on TV."
Mandela's widow, Graca Machel, received a huge ovation as she took her seat on the main stage constructed at one end of the pitch, while the entrance of President Jacob Zuma was roundly booed by a portion of the crowd. Mandela's ex-wife Winnie Madikizela-Mandela was also present. News of Mandela's death at his home in Johannesburg resonated around the world, triggering a wave of loving admiration from political and religious leaders, some of whom agree on little else.
(With inputs from PTI, AFP)