Childline founder and president Esther Rantzen said: "I would urge members of the public to consider becoming a Childline volunteer".
The charity says that it provided an average of 62 counselling sessions every day for children contemplating ending their own lives - some of them as young as ten years old.
Suicide is the third most common reason for girls to contact Childline, and the fifth most common for boys.
Two thousand children had already taken steps towards suicide, such as writing a note or planning a method, the NSPCC's advice line said.
The report also said that some young people described having difficulty getting NHS help from their local child and adolescent mental health service.
Elaine Chalmers, head of helplines for Childline in Scotland, said: "We must face the painful reality that many young people across Scotland and the United Kingdom feel so overwhelmed by their problems they have considered taking their own, precious lives".
"Anyone who can lend a few hours to this vital service could end up saving a child's life".
"We must face the painful reality that many young people across Scotland and the United Kingdom feel so overwhelmed by their problems they have considered taking their own, precious lives".
'We have never seen figures like these before and they are a blunt wake-up call.
A spokesman for the charity added: "Without appropriate support for young people, many are shouldering their troubles single-handedly and turning to Childline only when they reach crisis point". "Now young people tell us they are overwhelmed by mental health issues, taking them to the brink of suicide".
Childline in the United Kingdom can be reached on 0800 1111, or by confidential email via its website.