Community Land Scotland (CLS) said it also wants to see a new land agency established, equipped with compulsory purchase powers, to secure greater community ownership.
However, voluntary agreements between communities and landowners should be at the heart of its work, CLS said.
The organisation, which sees a future for tenant farmers under community ownership, also called for funding of the Scottish Land Fund, which supports community land ownership, to be increased by the Scottish Government from £6 million over three years to £10m a year.
The radical proposals, which will almost certainly be opposed by landowners, are contained in CLS's submission to Land reform Review Group set by ministers last year to advise them, among other things, on how more people can have in stake in controlling their land.
CLS currently supports the community owners of more than 500,000 acres of land acquired in the headline buyouts in the likes of Assynt, Eigg and Gigha.
It claims that, despite progress over recent years in the number of communities owning their land, the total of Scotland's land in community ownership remains a tiny fraction of all land holdings and the basic pattern of land ownership has changed little for generations.
The submission said: "Scotland's land ownership patterns are out of line with what would be the norm in most of Europe, or the rest of the world, with vast tracts of land owned by a tiny proportion of the population. This disempowers communities and does not promote achieving greater social justice.
"Current land reform legislation gives communities a right to buy local land whether the owner wants to sell, conditional on ministerial approval. CLS believes this right to buy should be extended across Scotland."
But CLS sees greatest potential not in hostile buyouts, but in negotiated land transfers, particularly where the community might not want to takeover a whole estate and the big house.
However, Paul Wakefield of the landowners' organisation Scottish Land and Estates, said "We would not support any extension of the community right to buy from the present provisions under the existing land reform legislation."