In the malaria parasite P. falciparum, drug resistance generally evolves first in low-transmission settings, such as Southeast Asia and South America. Resistance takes noticeably longer to appear in the high-transmission settings of sub-Saharan Africa, although it may spread rapidly thereafter. Here, we test the hypothesis that competitive suppression of drug-resistant parasites by drug-sensitive parasites may inhibit evolution of resistance in high-transmission settings, where mixed-strain infections are common. We employ a cross-scale model, which simulates within-host (infection) dynamics and between-host (transmission) dynamics of sensitive and resistant parasites for a population of humans and mosquitoes. Using this model, we examine the effects of transmission intensity, selection pressure, fitness costs of resistance, and cross-reactivity between strains on the establishment and spread of resistant parasites. We find that resistant parasites, introduced into the population at a low frequency, are more likely to go extinct in high-transmission settings, where drug-sensitive competitors and high levels of acquired immunity reduce the absolute fitness of the resistant parasites. Under strong selection from antimalarial drug use, however, resistance spreads faster in high-transmission settings than low-transmission ones. These contrasting results highlight the distinction between establishment and spread of resistance and suggest that the former but not the latter may be inhibited in high-transmission settings. Our results suggest that within-host competition is a key factor shaping the evolution of drug resistance in P. falciparum.