A blooming research agenda has begun examining the influence of party competition dynamics on politician social media behaviour. Most studies focus on the US context, generally finding little evidence that party competition dynamics influence which policy issues politicians attend to on these platforms. Instead, I turn to the Danish context and show how party competition dynamics exert a substantial influence on politicians' attention to issues in their tweets. First, I map the level of politician issue attention on Twitter across several years outside election campaigns. Second, I show that party issue ownership and the status of a party as a government or opposition party strongly influence politicians' attention to issues on the platform. Third, I provide novel insights into how the interplay between party issue ownership and internal party organisation influences politician issue attention on Twitter. The findings indicate that the tweets posted by politicians are an integral aspect of contemporary party competition.