Maybe it isn't surprising that one of the chief theorists of rights of sovereignty, Emeric de Vattel, was also a theorist of property rights. Vattel, of course, was an apologist for an expansionist absolutist state. His conception of sovereignty was rooted in the efficacy of the state governing any society: if a state exerted effective control over a territory, it had a right to govern within that territory. His version of property rights was rather similar. Nations, he suggested, are bound by natural law to cultivate the land within their reach, and if they do not, then they surrender their right to the territory. So, while the conquest of Peru and Mexico (of the Incas and Aztecs) was "a notorious usurpation", the peoples of the continent of North America had not so much inhabited those vast land tracts as roamed over them, and so the establishment of colonies was lawful "within just limits". That last qualification was not one that capitalist England was willing to accept, and not only because of the Puritan zeal of its colonists.
England had already begun the process of internal colonisation, that is of transferring property into the hands of the ruling class on the basis of doctrines of rightful appropriation, later formalised by Locke. The creation of value (that is of value realised in market transactions, exchange value) through labour was the basis of newly recognised rights of property. Property rights can occur only in the capitalist mode of production. There could be no question of "just limits" here, since anything that produced less value than English agricultural capitalism was wasteful. The English could no more co-exist with the Indians than capitalism can co-exist in the same borders for any length with hunter-gathering societies. No more than English capitalism could co-exist with Jacobite clansmen in the Scottish Highlands (several notorious and deliberately exemplary massacres were perpetrated in that war, and Dalrymple of Stair wasn't above considering genocide). Precisely because they pursued empire under specifically capitalist imperatives, the English relations with the Indians were genocidal.
This is not to say that the tributary 'encomienda' system set up by the Spanish in Peru, for instance, was all sweetness and light. Their attrition with those they sought to exploit and occupy over long periods was massively genocidal in effect, destroying tens of millions of lives. But the English drive to accumulate under capitalist imperatives became a drive to displace the local population rather than cohabit with them. This was very different to the contiguous French colonisation, which never degenerated to the barbarous depths of the English colonies. And this became part of the official American ideology as it expanded inwardly. "Common property and civilization cannot co-exist," a Commissioner for Indian Affairs explained in 1838. In practise, this meant that Indians were driven into reservations that resembled nothing so much as the concentration camps later used by the American government against Japanese citizens during World War II.
"Property rights" in the capitalist sense, aside from being a chimera, is a synonym for barbarism.