The Scotland Institute is calling for local councils to provide early years education in primary schools for four-year-olds, arguing this could provide an "excellent and equitable transition to more formal education".
Dr Azeem Ibrahim, the Institute's executive chairman, insisted there were "long term educational benefits for four-year-olds" from such a move, adding it was not about "simply providing low cost child minding".
The Scottish Government pointed out many children already start school at the age of four, adding it was "difficult to see" how the change would enhance existing childcare plans.
But in its report Early Start 4 Scotland, the Scotland Institute said there was "substantial evidence that young children in Scotland are already unequal in terms of their educational achievement by the time they enter formal schooling at five".
While it said the Scottish Government had accepted the importance of early years education, it added there was "little evidence that this has addressed the deep-seated problem that children from poorer backgrounds have already fallen behind by the time they start primary school".
It also said the current 475 hours of free childcare three and four year olds are entitled to was "inadequate", with research showing 60% of parents they require closer to 1,000 hours of care.
The think-tank is calling for all four-year-olds to attend pre-school, with empty space in primary schools to be used for this.
The Scotland Institute said there was capacity within Scotland's primary schools to allow for "a substantial expansion of usage", adding that 21% of primary schools - 433 schools - are half full or less.
Dr Ibrahim said the report called on the Scottish Government "to implement the practical strategy of making use of existing spare capacity in primary schools to provide four-year-olds with an excellent and equitable transition to more formal education".
He added that this could be achieved by changing councils' responsibilities, so they no longer commissioned early years education at local nurseries and instead actually provide this themselves.
"By creating universal provision at age four, we can ensure equity of provision and remove some of the barriers to educational achievement by giving this age group a head start," Dr Ibrahim said.
"There is plenty of evidence from other countries that this can significantly reduce future social problems and can help level the playing field for low-income children.
"We also recommend that local councils cease to commission child care and instead provide it within our primary schools, to ensure that there are long term educational benefits for four-year-olds instead of simply providing low-cost child minding."
He added: "Our report makes it clear that the provision of high quality early child care and education will reduce child poverty in the long run."
Holyrood recently passed legislation which will increase the amount of childcare three and four year olds receive to 600 hours a year, with the SNP also having set out its ambition to up this to 1,140 hours if Scotland becomes independent.
A Scottish Government spokesman said: "Many Scottish pupils already start school aged four where their parents feel that is the right thing for them and Curriculum for Excellence is now in place and covers ages of three to 18, including nurseries.
"What's more, it is already our plan, with independence, to give pre-school children the same number of hours in nursery as primary children.
"As a result, it is a little difficult to see how this report adds anything to existing plans."