Biological invasions often transcend political boundaries, but the capacity of countries to prevent invasions varies. How this variation in biosecurity affects the invasion risks posed to the countries involved is unclear. We aimed to improve the understanding of how the biosecurity of a country influences that of its neighbours. We developed six scenarios that describe biological invasions in regions with contiguous countries. Using data from alien species databases, socio‐economic and biodiversity data and species distribution models, we determined where 86 of 100 of the world's worst invasive species are likely to invade and have a negative impact in the future. Information on the capacity of countries to prevent invasions was used to determine whether such invasions could be avoided. For the selected species, we predicted 2,523 discrete invasions, most of which would have significant negative impacts and are unlikely to be prevented. Of these invasions, approximately a third were predicted to spread from the country in which the species first establishes to neighbouring countries where they would cause significant negative impacts. Most of these invasions are unlikely to be prevented as the country of first establishment has a low capacity to prevent invasions or has little incentive to do so as there will be no impact in that country. Regional biosecurity is therefore essential to prevent future harmful biological invasions. In consequence, we propose that the need for increased regional co‐operation to combat biological invasions be incorporated in global biodiversity targets.