Generating SPARQL queries is crucial for extracting relevant information from diverse knowledge graphs. However, the structural and semantic differences among these graphs necessitate training or fine-tuning a tailored model for each one. In this paper, we propose UniQ-Gen, a unified query generation approach to generate SPARQL queries across various knowledge graphs. UniQ-Gen integrates entity recognition, disambiguation, and linking through a BERT-NER model and employs cross-encoder ranking to align questions with the Freebase ontology. We conducted several experiments on different benchmark datasets such as LC-QuAD 2.0, GrailQA, and QALD-10. The evaluation results demonstrate that our approach achieves performance equivalent to or better than models fine-tuned for individual knowledge graphs. This finding suggests that fine-tuning a unified model on a heterogeneous dataset of SPARQL queries across different knowledge graphs eliminates the need for separate models for each graph, thereby reducing resource requirements.