The purpose of this study is to assess how large language models (LLMs) can be used for fact-checking and contribute to the broader debate on the use of automated means for veracity identification. To achieve this purpose, we use AI auditing methodology that systematically evaluates performance of five LLMs (ChatGPT 4, Llama 3 (70B), Llama 3.1 (405B), Claude 3.5 Sonnet, and Google Gemini) using prompts regarding a large set of statements fact-checked by professional journalists (16,513). Specifically, we use topic modeling and regression analysis to investigate which factors (e.g. topic of the prompt or the LLM type) affect evaluations of true, false, and mixed statements. Our findings reveal that while ChatGPT 4 and Google Gemini achieved higher accuracy than other models, overall performance across models remains modest. Notably, the results indicate that models are better at identifying false statements, especially on sensitive topics such as COVID-19, American political controversies, and social issues, suggesting possible guardrails that may enhance accuracy on these topics. The major implication of our findings is that there are significant challenges for using LLMs for factchecking, including significant variation in performance across different LLMs and unequal quality of outputs for specific topics which can be attributed to deficits of training data. Our research highlights the potential and limitations of LLMs in political fact-checking, suggesting potential avenues for further improvements in guardrails as well as fine-tuning.