This paper explores the discourse of the Russia–Ukraine war to outline the dominant narrative schemas anchored in the spatial geopolitical representations of globalness and localness. It uses tools from the domains of critical cognitive discourse studies and narrative research (alternative futures, discourse scenarios, deictic space, proximization) to distinguish between two most salient schemas: the Global Conflict Reality (GCR) narrative and the Local Conflict Reality (LCR) narrative. The GCR narrative conceptualizes the Russia–Ukraine war as a growing international conflict, producing serious political, economic and material consequences for the global community. GCR uses coercive rhetoric to call for immediate measures to support Ukraine so the war can be stopped before spreading beyond its current borders. The principal narrator of GCR is Ukraine, though the narrative is re-contextualized in other countries located in geographical proximity to the conflict. The LCR narrative, performed mostly by the Kremlin, construes the war as a local conflict providing no reasons for foreign intervention. LCR is distinctive for its large number of sub-narratives appropriated for different geopolitical audiences, which include the Russian and Ukrainian people, and different audience groups in the West and the Global South. The latter groups re-contextualize the LCR narrative, focusing primarily on economic issues.