Supervised named entity recognition (NER) in the biomedical domain is dependent on large sets of annotated texts with the given named entities, whose creation can be time-consuming and expensive. Furthermore, the extraction of new entities often requires conducting additional annotation tasks and retraining the model. To address these challenges, this paper proposes a transformer-based method for zero- and few-shot NER in the biomedical domain. The method is based on transforming the task of multi-class token classification into binary token classification (token contains the searched entity or does not contain the searched entity) and pre-training on a larger amount of datasets and biomedical entities, from where the method can learn semantic relations between the given and potential classes. We have achieved average F1 scores of 35.44% for zero-shot NER, 50.10% for one-shot NER, 69.94% for 10-shot NER, and 79.51% for 100-shot NER on 9 diverse evaluated biomedical entities with PubMedBERT fine-tuned model. The results demonstrate the effectiveness of the proposed method for recognizing new entities with limited examples, with comparable or better results from the state-of-the-art zero- and few-shot NER methods.