Paul Kagame, who led a rebel force that ended the slaughter, lit a remembrance flame in the capital Kigali.
Rwandans will mourn for 100 days, the time it took in 1994 for about a tenth of the country to be massacred.
Most of those who died were minority Tutsis and moderate Hutus, killed by ethnic Hutu extremists.
“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.”
How is Rwanda remembering?
The commemoration activities began with the flame-lighting ceremony at the memorial. The flame will burn for 100 days.
The 61-year-old president, who has led the country since 2000, then delivered a speech at the Kigali Convention Centre.
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.”
Mr Kagame then led a vigil at the Amahoro National Stadium, which was used by United Nations officials to try to protect Tutsis during the killings.
About 2,000 people marched together on a walk of remembrance from parliament to the stadium, where candles were lit.
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