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Exploring and quantifying semantic relatedness is central to representing language and holds significant implications across various NLP tasks. While earlier NLP research primarily focused on semantic similarity, often within the English language context, we instead investigate the broader phenomenon of semantic relatedness. In this paper, we present SemRel, a new semantic relatedness dataset collection annotated by native speakers across 13 languages: Afrikaans, Algerian Arabic, Amharic, English, Hausa, Hindi, Indonesian, Kinyarwanda, Marathi, Moroccan Arabic, Modern Standard Arabic, Spanish, and Telugu. These languages originate from five distinct language families and are predominantly spoken in Africa and Asia - regions characterised by a relatively limited availability of NLP resources. Each instance in the SemRel datasets is a sentence pair associated with a score that represents the degree of semantic textual relatedness between the two sentences. The scores are obtained using a comparative annotation framework. We describe the data collection and annotation processes, challenges when building the datasets, baseline experiments, and their impact and utility in NLP.