Boris Johnson has warned that the UK "can't get complacent" about anti-Semitism, in a statement to mark Holocaust Memorial Day.
He was speaking after a virtual meeting with a Holocaust survivor and a soldier who liberated a Nazi death camp.
The prime minister described their testimonies as "perhaps the most powerful things I have ever heard".
People are being asked to light a candle in their window at 8pm to mark Holocaust Memorial Day.
The international date is for people to remember the millions murdered under Nazi persecution during World War Two, and the victims of subsequent genocides in Cambodia, Rwanda, Bosnia and Darfur.
This year's theme, chosen by the Holocaust Memorial Day Trust, is "be the light in the darkness", to encourage people to reflect on the depths to which humanity can sink.
Mr Johnson spoke to Renee Salt, a survivor of both the Auschwitz-Birkenau and Bergen-Belsen camps, and war veteran Ian Forsyth during a video call from Downing Street.
In the call, the pair described their memories of the camps.
Mrs Salt told the prime minister: "All the children, old people, pregnant women, invalids, all went to the right.
"I went to the left... left to live, right to die. I was together with my mother, for which I was very grateful, and so was she. Without my mother, I would never have survived."
Mr Forsyth wept as he recalled arriving in Bergen-Belsen in April 1945 to liberate the survivors.
He said: "We didn't even know the camp was there.
"When we got up that morning - a beautiful morning, I can remember that - my tank happened to be the lead tank on that particular day, but no-one told us what to expect.
"I'm sorry, I get very emotional when I talk about this.
"We came along the road and cut over across the fields, there was this camp in front of us.
"I've been back quite a few times, it draws me like a magnet."
Mr Johnson told them: "People get complacent about anti-Semitism. I think in the UK we can get complacent about it and we mustn't.
"It's so vital that you both have had the courage to continue to share with everybody, with me and the world, your memories of what took place. We can never forget it.
"Your personal memories have been perhaps the most powerful things I've ever heard.
"What you saw and experienced is horrifying and we must make sure nothing like that happens again."
At Prime Minister's Questions, Labour leader Sir Keir Starmer said he would be taking part in the candle-lighting ceremony "to remember the six million Jews murdered in the Holocaust, along of course with the other genocides and persecutions that have taken place around the world".
The SNP's Westminster leader Ian Blackford said "we must never forget" the six million Jews who lost their lives or "indeed those that have sadly followed them in genocides around the world".
Commons speaker Sir Lindsay Hoyle held a short candle-lighting ceremony for MPs in Portcullis House, the first time such an event has been held on the Parliamentary Estate for Holocaust Memorial Day.
He urged colleagues to "stand together, especially with those who are suffering".