Its conference is being led by UK Prime Minister David Cameron and Microsoft tycoon Bill Gates.
Mr Cameron will pledge to increase UK funding for global vaccination.
The UK has already committed more resources - £2bn over 30 years - than any other nation, including the US.
'Expertise' But on Sunday, writing in the Observer newspaper, Mr Cameron said there was a moral reason why action should be taken to prevent children dying from common diseases.
"We would not stand for that at home. And we should not stand for it anywhere, especially as Britain has the tools, the expertise, and yes, the money, to stop it happening."
Two million under-fives die from pneumonia alone each year despite the existence of a vaccine to protect them.
Organisers of the conference say the lives of an about four million children rest on the outcome of the gathering.It is estimated that three times as many children aged under five die from pneumonia and diarrhoea than from malaria and HIV/Aids combined, despite new vaccines being available to help prevent such deaths. However, many developing countries cannot afford them.
Drugs company GlaxoSmithKline last week agreed to sell a vaccine for diarrhoeal disease at cost price to poorer nations, and some other firms have since made similar moves.
Gavi has already rolled out a range of vaccines to children in 19 countries but the organisation says it has not got the £2.3bn needed to vaccinate those in 26 others.
This leaves the lives of four million children at risk, it says.
Resources will also be spent on trying to reach millions of the poorest children who are missing out on basic vaccines against diseases such as measles, whooping cough and tetanus.
Gavi is a health partnership of governments, businesses, and bodies including the World Bank, Unicef and Mr Gates' personal foundation.
'Make-or-break' Ahead of Monday's conference, the philanthropist said: "This is my life's work, and days like tomorrow energise us to do even better. I think a success would create incredible momentum.
"I know that the whole image of aid can be saved if people know it's about saving lives."
The Save the Children charity says the leaders at the conference have a "make-or-break opportunity".
Chief executive Justin Forsyth said: "We are on the cusp of an historic breakthrough that would save millions of lives.
"We have new vaccines to tackle appalling common childhood killers like diarrhoea and more children than ever are getting immunised against illnesses like whooping cough. But without pledges, that incredible progress could stall."
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