The aim of this study is to examine how transformational and transactional leaders, boost the employees’ innovative work behaviour, directly or through work engagement, organizational climate for innovation and absorptive capacity in Latin American firms. A non-random sample of 1429 employees was used who had been working at least one year in the current company. The sample, composed of workers from different industries, was collected in postgraduate programs of business schools from seven Latin American countries. A multi-group structural equation model was built with the involved variables, which adopted two different conditions: i.e., unconstrained and constrained questionnaire measurement weights. According to the results, leadership by itself is insufficient to promote employees innovative work behaviour. Transformational and transactional leadership exert effect on this behaviour only through absorptive capacity and work engagement respectively. Likewise, absorptive capacity and employee work engagement show direct effects on innovative work behaviour. Additionally, organizational climate for innovation shows a significant moderating effect on the all relationships included in the model. Despite the cultural differences, the two-condition model yielded the same effect in each country, which indicates the validity of a general model of innovative work behaviour for the whole region supporting the common identity of this region. As a conclusion, leadership practices are needed to encourage innovative work behaviour within the Latin American organizational context, however some individual (engagement) and organizational (absorptive capacity) conditions are also needed to ensure this effect. Implications for human resources management are discussed.