The ceremony comes at the start of a week of events
Rwanda has held a candlelit vigil at the start of a week of national mourning to mark 15 years since the genocide which killed 800,000 people.
Ceremonies were held in the capital Kigali, and in Nyanza, where more than 5,000 people were slaughtered.
At a stadium in Kigali, thousands of candles spelt out the word "hope" in three languages.
UN Secretary General Ban Ki-moon has said that preventing future genocide was "a collective responsibility".
"Only by meeting this challenge can we match the resolve of the survivors and truly honour the memory of those who died in Rwanda 15 years ago," he said.
"The resounding voices of survivors touch us in ways that no other words could. Yet the silence of the more 800,000 innocent victims still haunts our collective conscience."
Karen Allen at the genocide vigil
US President Barack Obama said the genocide was "so enormous, so daunting, that it runs the risk of becoming a statistic".
He said it was important to remember that each person who died had "their own story, their own family, and their own dreams" and that remembering such events deepened the commitment to prevent "future atrocities".
Mr Obama also praised the "courageous" survivors who he said had "demonstrated remarkable strength and generosity in forgiving those who committed these heinous acts".
"These individuals inspire us daily by working to restore trust and rebuild hope in Rwanda," he said.
'Cowardice'
RWANDA'S 1994 GENOCIDE
6 April:
Rwandan Hutu President Habyarimana's plane shot down
April-July:
An estimated 800,000 Tutsis and moderate Hutus killed
July:
Tutsi-led rebel group RPF captures Rwanda's capital Kigali
July:
Two million Hutus flee to Zaire, now DR Congo
The BBC's Karen Allen, in the Kigali stadium, said the ceremony was very emotional, with several people overcome by grief and having to be carried out.
Dignitaries and ordinary Rwandans, led by Mr Kagame, queued up to light candles.
"We must remember, but life must go on," Mr Kagame told the crowd.
"We must continue to build a better future."
But Mr Kagame has also used the occasion to accuse the international community of cowardice and of abandoning Rwandans to their deaths.
Several people were overcome by emotion at the ceremonies
He laid a wreath and lit a torch at the scene of a massacre in Nyanza, seen by many as a symbol of the UN's failure 15 years ago.
The killings there took place after Belgian troops withdrew following a Rwandan militia attack that claimed the lives of 10 peacekeepers on 7 April that year.
Mr Kagame said the people of Rwanda had been "abandoned in their time of need" by the UN troops sent to protect them.
"They left them to be murdered. Aren't they guilty?", AFP quoted him as saying.
"They left even before any shot was fired."
He said the international community was "part of that history and the root causes of the genocide," but that Rwandans were "not like those who abandoned people they had come to protect".
Tribunals
The genocide in Rwanda began when President Juvenal Habyarimana's plane was shot down on 6 April 1994.
In many ways, the perpetrators of the genocide have succeeded
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