Echoing the words of Nelson Mandela following his release from prison, Dr John Sentamu urged people to unite as a community in a bid to get to the truth of what happened in the disaster six weeks ago.
He attended the service alongside relatives and friends of five of those killed in the blaze, including two child victims.
The lives of artist Khadija Saye, her mother Mary Mendy, Berkti Haftom and her 12-year-old son Beruk, as well as five-year-old Isaac Paulos were being celebrated at the ecumenical service in north Kensington.
During the course of two hours, tributes were paid to the five, and some frustrations vented at the "disgusting" tragedy that claimed at least 80 lives and left a gutted 24-storey tower block described by one relative as a "tall coffin in the air".
During and after the service at St Helen's Church, little more than half a mile from the site of the fire, Dr Sentamu spoke of his hope for survivors to find truth, justice and reconciliation.
Speaking afterwards, he told the Press Association: "My plea with them is the words of Nelson Mandela to young people in South Africa when they were getting very angry when he came out of prison and he said to young people 'I understand your anger. May I plead with you, anger is energy, you can either destroy or build. Use your anger for creativity, together as a community, come together and nobody will destroy you.'
"So I'm hoping that now is the time for the people in the community to come together so that truth emerges, justice happens, reconciliation happens."
The forthcoming public inquiry into the tragedy has endured a turbulent start, with survivors and campaigners claiming that Sir Martin Moore-Bick, the retired Court of Appeal judge leading the process, is unfit for the role.
But Dr Sentamu urged people not to rush to judgment.
He said: "I've looked at the cases he has tried and I have got no reason to doubt that he was a very high-ranking judge, he is not likely to be changing his spots now that he's got to this stage, and if people have got concerns it can actually be addressed."
The archbishop was clapped when he told the congregation no stone must be left unturned in the quest for justice.
He said: "All of the stones, all of the tiny things, like a grain of sand, must be turned in order to discover the truth.
"Because truth sets all of us free. And when truth is discovered then the possibility for justice can be there and the possibility for reconciliation."
Thursday's service had music from the Gospel For Grenfell choir who sang a number of well-known songs including Something Inside So Strong.
Ms Saye's cousin Adelaide Mendy recalled the fear and panic on the night of the fire, and her desperate hope that her relatives would not be caught up in it.
She told those gathered: "I felt an excruciating and an almost unbearable pain. I felt powerless at the thought that there was nothing else that I could've done."
She said Grenfell Tower had been a place of happy memories for her, before the destruction and terror caused by the fire.
She said: "The flats where families got together for parties and where social gatherings were held. A place where love was given and received, where endless joy was felt.
"That happy place. Now stands a war zone, dipped in blood, black, filled with ashes and skeletons. With the silent voices that will never be heard."
She paid tribute to her cousin and aunt, saying Ms Saye's love for art and her work had "inspired people to do better and make a difference".
A tribute read on behalf of David Lammy MP, a family friend, recalled the pair as "two beautiful souls".
Another cousin, Ambrose Mendy, gave a passionate speech in which he described the disaster as "a disgrace" and "disgusting".
He said: "People's lives have been taken away from them, generations of hope, homes which people have invested their life in, are gone.
"This tall coffin in the air, is perhaps the best way to describe it. What's going to happen to it? How long is it going to remain there as a timely reminder of man's inhumanity to man?"
Ms Mendy was described by her brother Paul as a "hard-working single mother whose love for her only daughter knew no bounds".
Father Georgis Dimtsu, speaking on behalf of the Haftom and Paulos families, said their deaths had been a huge loss to the Ethiopian community.
He described Isaac, also know by the surname Welde Mariam, and Beruk as "brilliant students".
Alluding to what he described as a culture in Ethiopia of hopes for bright, young people to enter the medical profession, he said: "Beruk, we were hoping he will be a successful doctor, so as Isaac.
"We didn't expect this would happen. It's unfortunate. For the Ethiopian community it is a big loss. It is terrifying, it's tragic."
The families left the service to a recording of Michael Jackson's You Are Not Alone.
