Large language models (LLMs) have gained considerable attention for Artificial Intelligence Generated Content (AIGC), particularly with the emergence of ChatGPT. However, the direct adaptation of continuous speech to LLMs that process discrete tokens remains an unsolved challenge, hindering the application of LLMs for speech generation. The advanced speech LMs are in the corner, as that speech signals encapsulate a wealth of information, including speaker and emotion, beyond textual data alone. Prompt tuning has demonstrated notable gains in parameter efficiency and competitive performance on some speech classification tasks. However, the extent to which prompts can effectively elicit generation tasks from speech LMs remains an open question. In this paper, we present pioneering research that explores the application of prompt tuning to stimulate speech LMs for various generation tasks, within a unified framework called SpeechGen, with around 10M trainable parameters. The proposed unified framework holds great promise for efficiency and effectiveness, particularly with the imminent arrival of advanced speech LMs, which will significantly enhance the capabilities of the framework. The code and demos of SpeechGen will be available on the project website: \url{https://ga642381.github.io/SpeechPrompt/speechgen}