This paper describes the system we developed for SemEval-2024 Task 1, "Semantic Textual Relatedness for African and Asian Languages." The aim of the task is to build a model that can identify semantic textual relatedness (STR) between two sentences of a target language belonging to a collection of African and Asian languages. We participated in Subtasks A and C and explored supervised and cross-lingual training leveraging large language models (LLMs). Pre-trained large language models have been extensively used for machine translation and semantic similarity. Using a combination of machine translation and sentence embedding LLMs, we developed a unified STR model, TranSem, for subtask A and fine-tuned the T5 family of models on the STR data, FineSem, for use in subtask C. Our model results for 7 languages in subtask A were better than the official baseline for 3 languages and on par with the baseline for the remaining 4 languages. Our model results for the 12 languages in subtask C resulted in 1st place for Africaans, 2nd place for Indonesian, and 3rd place for English with low performance for the remaining 9 languages.