The Church and ten other organisations have written the letter following the death of a homeless man in Glasgow after a bitterly cold night.
The groups said the case highlights the need for a new national homelessness strategy to be brought forward by ministers.
They wrote: "This was not the first such story and it will not be the last. It is a badge of shame that homelessness still exists in our society.
"We the undersigned are profoundly concerned by the current lack of political leadership and urgency in relation to tackling homelessness in Scotland today.
"Without decisive action, we are endangering the lives of a growing number of people forced to sleep rough on the streets of our towns and cities, and condemning many more individuals and families to a life in limbo, by forcing them to stay for increasing lengths of time in so-called temporary accommodation.
"There is now a real danger of squandering the legacy of Scotland's world-leading 2012 commitment on homelessness - which gave everyone the right to a settled home."
The organisations recommend the Scottish Government should prioritise closing the education attainment gap, improving health outcomes, eradicating child poverty and reducing reoffending.
A Scottish Government spokesman said: "Any death in these circumstances is a tragedy and our sympathy and condolences are with this young man's friends and family.
"We have some of the strongest housing rights for homeless people in the world and will continue to work strategically across government and with national partners, to tackle homelessness.
"We are proud that Scotland's legislation and preventative approach means everyone has the right to temporary accommodation."
According to Shelter Scotland, almost 35,000 people are homeless in Scotland.