"In 1994, there was no hope, only darkness," Mr Kagame told a crowd gathered at the Kigali Genocide Memorial, where more than 250,000 victims are thought to be buried.
"Today, light radiates from this place. How did it happen? Rwanda became a family once again."
He said the resilience and bravery of the genocide survivors represented the "Rwandan character in its purest form".
"The arms of our people, intertwined, constitute the pillars of our nation," he said. "We hold each other up. Our bodies and minds bear amputations and scars, but none of us is alone.
"Together, we have woven the tattered threads of our unity into a new tapestry."
He added: "The fighting spirit is alive in us. What happened here will never happen again."
There was a moment - when all the candles were lit, and their lights bobbed around the stadium, when people were taking pictures with their smartphones - when it was almost possible to forget the horror that brought thousands of people together on this warm evening in Kigali.
"Well," he said, "it's important." In the understated way which so many people in Rwanda speak he said: "I lost people. I lost my parents. I lost my siblings."
French President Emmanuel Macron did not go, however. This week he appointed a panel of experts to investigate France's role in the genocide.
Olive Muhorakeye, 26, told Reuters: "Remembering is necessary because it's only thanks to looking back at what happened [can we] ensure that it never happens again."
One of the militias was the ruling party's youth wing, the Interahamwe, which set up road blocks to find Tutsis, incited hatred via radio broadcasts and carried out house to house searches.
But the country has recovered economically, with President Kagame's policies encouraging rapid growth and technological advancement.
Growth remains good - 7.2% in 2018 according to the African Development Bank.
But Mr Kagame's critics say he is too authoritarian and does not tolerate dissent.