Large Language Models (LLMs) frequently hallucinate, impeding their reliability in mission-critical situations. One approach to address this issue is to provide citations to relevant sources alongside generated content, enhancing the verifiability of generations. However, citing passages accurately in answers remains a substantial challenge. This paper proposes a weakly-supervised fine-tuning method leveraging factual consistency models (FCMs). Our approach alternates between generating texts with citations and supervised fine-tuning with FCM-filtered citation data. Focused learning is integrated into the objective, directing the fine-tuning process to emphasise the factual unit tokens, as measured by an FCM. Results on the ALCE few-shot citation benchmark with various instruction-tuned LLMs demonstrate superior performance compared to in-context learning, vanilla supervised fine-tuning, and state-of-the-art methods, with an average improvement of $34.1$, $15.5$, and $10.5$ citation F$_1$ points, respectively. Moreover, in a domain transfer setting we show that the obtained citation generation ability robustly transfers to unseen datasets. Notably, our citation improvements contribute to the lowest factual error rate across baselines.