Large language models (LLMs) demonstrate remarkable machine translation (MT) abilities via prompting, even though they were not explicitly trained for this task. However, even given the incredible quantities of data they are trained on, LLMs can struggle to translate inputs with rare words, which are common in low resource or domain transfer scenarios. We show that LLM prompting can provide an effective solution for rare words as well, by using prior knowledge from bilingual dictionaries to provide control hints in the prompts. We propose a novel method, DiPMT, that provides a set of possible translations for a subset of the input words, thereby enabling fine-grained phrase-level prompted control of the LLM. Extensive experiments show that DiPMT outperforms the baseline both in low-resource MT, as well as for out-of-domain MT. We further provide a qualitative analysis of the benefits and limitations of this approach, including the overall level of controllability that is achieved.