Storybook reading accompanied by adult-guided conversation provides a stimulating context for children's language development. Conversational agents powered by artificial intelligence, such as smart speakers, are prevalent in children's homes and have the potential to engage children in storybook reading as language partners. However, little research has explored the effectiveness of using conversational agents to support children's language development. This study examined how an automated conversational agent can read stories to children via a smart speaker while asking questions and providing contingent feedback. Using a randomized experiment among 90 children aged three to six years, this study compared these children's story comprehension and verbal engagement in storybook reading with a conversational agent versus an adult. The conversational agent's guided conversation was found to be as supportive in improving children's story comprehension as that provided by an adult language partner. At the same time, this study uncovered a number of differences in children's verbal engagement when interacting with a conversational agent versus with an adult. Specifically, children who read with the conversational agent responded to questions with better intelligibility, whereas those who read with an adult responded to questions with higher productivity, lexical diversity, and topical relevance. And the two groups responded to questions with a similar level of accuracy. In addition, questions requiring high cognitive demand amplified the differences in of verbal engagement between the conversational agent and adult partner. The study offers important implications for developing and researching conversational agent systems to support children's language development.