Counterspeech has been demonstrated to be an efficacious approach for combating hate speech. While various conventional and controlled approaches have been studied in recent years to generate counterspeech, a counterspeech with a certain intent may not be sufficient in every scenario. Due to the complex and multifaceted nature of hate speech, utilizing multiple forms of counter-narratives with varying intents may be advantageous in different circumstances. In this paper, we explore intent-conditioned counterspeech generation. At first, we develop IntentCONAN, a diversified intent-specific counterspeech dataset with 6831 counterspeeches conditioned on five intents, i.e., informative, denouncing, question, positive, and humour. Subsequently, we propose QUARC, a two-stage framework for intent-conditioned counterspeech generation. QUARC leverages vector-quantized representations learned for each intent category along with PerFuMe, a novel fusion module to incorporate intent-specific information into the model. Our evaluation demonstrates that QUARC outperforms several baselines by an average of ~10% across evaluation metrics. An extensive human evaluation supplements our hypothesis of better and more appropriate responses than comparative systems.