This study integrates agenda setting and framing theory to explore the transmission of climate change frames between newspapers and Twitter in the US and the UK. A set of computational methods was applied to identify five prevailing climate change frames—cause, impact, action, real, and hoax—in 230,000 tweets and 20,000 news articles from 2016 to 2021. At the cross-national level, a symmetrical relationship was found on Twitter between the US and the UK, which indicates their mutual influence on social-media discussions of climate change. Within each country, the US news media had a stronger agenda-setting influence on public climate change discussions on Twitter, whereas news coverage and social-media discussions in the UK were relatively isolated. The use of the cause frame in the US media coverage often led to the presence of the hoax, action, impact, and cause frames in Twitter conversations, whereas the action frame in the UK media coverage led to the presence of the hoax, real, and impact frames in Twitter discussions. The findings have implications for the dynamics of framing processes that shape public attention and the understanding of climate issues cross-nationally.