David Cameron said he was awestruck by the dedication of those who survived the death camps, who have shared their memories of the horrors they suffered to ensure that future generations do not forget them.
He made the comments ahead of a meeting of hundreds of survivors of Nazi persecution, being held in London today as part of the Holocaust Commission set up by the Government.
The meeting, believed to be one of the largest gatherings of survivors ever held in Britain, will hear ideas about how the Holocaust should be remembered.
Mr Cameron said: "I am awestruck by the work that so many survivors do teaching our young people about the Holocaust.
"We must ensure the memory and the lessons of the Holocaust are never forgotten.
"This event is important because it gives the commission the chance to hear from survivors first-hand about how to best commemorate the Holocaust and to educate future generations of every faith and none. With their help we can ensure that the memory and the lessons of the Holocaust live on for generations to come."
The commission has been set up to investigate what more needs to be done to ensure Britain has a fitting memorial to the Holocaust and the right educational resources to educate future generations about the genocide, in which an estimated six million Jews were slaughtered.
Actress Helena Bonham Carter, whose grandfather Eduardo Propper de Callejon helped thousands of Jews flee from occupied France during the war, is part of the project.
It is due to report its findings to Mr Cameron at the end of the year -- in time for the 70th anniversary of the British liberation of Bergen-Belsen concentration camp next April.