“I want to make sure Parag is doing everything possible to build towards your goals until close” Mr. Dorsey wrote in a message to Mr. Musk dated April 26. “He is really great at getting things done when tasked with specific direction.”

The text messages also show that Mr. Dorsey tried to get Mr. Musk on the Twitter board before the Tesla Inc. CEO’s acquiring a significant stake in the company earlier this year. In a text exchange from the end of March, Mr. Dorsey wrote to Mr. Musk: “I tried my hardest to get you on our board, and board said no. That’s about the time I decided I needed to work to leave, as hard as it was for me.”

Mr. Dorsey stepped down as Twitter’s CEO at the end of November and left the board in May.

The Wall Street Journal previously reported that Mr. Dorsey had been part of a shadow crew that was encouraging Mr. Musk’s takeover of the company behind the scenes. The texts disclosed Thursday provide more details of Mr. Musk and Mr. Dorsey’s thinking about the future of the platform and Mr. Musk’s possible takeover.

Twitter didn’t immediately respond to a request for comment. Representatives of Mr. Musk and Mr. Dorsey didn’t immediately respond to requests for comment.

Mr. Dorsey’s efforts to smooth a relationship between Mr. Musk and Mr. Agrawal appear to have been short-lived, according to the texts made public Thursday. Mr. Dorsey, identified in the filing as “jackjack,” offered to set up a phone call between Mr. Musk and Mr. Agrawal “to discuss next steps and get really clear on what’s needed.”

Mr. Agrawal “would be able to move fast and clear then. Everyone is aligned and this will help even more,” Mr. Dorsey wrote, according to the court documents.

After the call, Mr. Musk texted Mr. Dorsey: “Parag is just moving far too slowly and trying to please people who will not be happy no matter what he does.”

Mr. Dorsey responded: “At least it became clear that you can’t work together. That was clarifying.”

In May, Mr. Musk tweeted that the deal was temporarily on hold amid concerns over the number of fake and spam accounts on the platform. Mr. Agrawal posted his own series of tweets explaining how the company handles spam and bots.

Mr. Musk responded with multiple tweets, including one that was solely a poop emoji.

Mr. Dorsey has publicly shared his support for Mr. Musk’s ownership of Twitter. Hours after Mr. Musk’s agreement was announced, he framed it as a liberation from the grip of public ownership and advertising.

“Twitter as a company has always been my sole issue and my biggest regret. It has been owned by Wall Street and the ad model,” Mr. Dorsey tweeted on April 25. “Taking it back from Wall Street is the correct first step.”

“Solving for the problem of it being a company however, Elon is the singular solution I trust,” Mr. Dorsey wrote. “I trust his mission to extend the light of consciousness.”

Write to Meghan Bobrowsky at meghan.bobrowsky@wsj.com