There is substantial concern about the ability of advanced artificial intelligence to influence people's behaviour. A rapidly growing body of research has found that AI can produce large persuasive effects on people's attitudes, but whether AI can persuade people to take consequential real-world actions has remained unclear. In two large preregistered experiments N=17,950 responses from 14,779 people), we used conversational AI models to persuade participants on a range of attitudinal and behavioural outcomes, including signing real petitions and donating money to charity. We found sizable AI persuasion effects on these behavioural outcomes (e.g. +19.7 percentage points on petition signing). However, we observed no evidence of a correlation between AI persuasion effects on attitudes and behaviour. Moreover, we replicated prior findings that information provision drove effects on attitudes, but found no such evidence for our behavioural outcomes. In a test of eight behavioural persuasion strategies, all outperformed the most effective attitudinal persuasion strategy, but differences among the eight were small. Taken together, these results suggest that previous findings relying on attitudinal outcomes may generalize poorly to behaviour, and therefore risk substantially mischaracterizing the real-world behavioural impact of AI persuasion.