Twitter's stock price rises at the end of trading after Elon Musk withdraws from board appointment.

• On Saturday morning, Elon Musk announced that he would not be joining Twitter's board of directors.
• On Sunday, Parag Agrawal, CEO of Twitter, publicly declared that Elon Musk remains the largest shareholder of the company and that Twitter will continue to value his input.

Despite CEO Parag Agrawal's announcement that Elon Musk had abandoned his plan to join the company's board, the stock remained positive at the close Monday.

At 4 a.m. ET, Twitter's stock price dropped more than 8% to less than $43 a share before recovering. Despite fluctuations throughout the day, Twitter's shares ended up closing with a 1.7% gain at $47.01.

On April 5, Twitter announced that Elon Musk would be joining its board. The previous day, Musk, the CEO of SpaceX, disclosed through financial filings that he holds a 9.2% stake in the company.

On Saturday, Twitter had planned to appoint Musk to its board, but Musk informed the company that he would not be accepting the position.

""Elon has opted not to join our board," Agrawal announced on Twitter on Sunday."

Agrawal stated that Musk continues to be the largest shareholder of Twitter and the company will remain receptive to his feedback.

"He wrote that we were excited to collaborate and clear about the risks. Additionally, we believed that having Elon as a fiduciary of the company, where he, like all board members, had to act in the best interests of the company and all our shareholders, was the best path forward."

Agrawal did not specify if Musk provided specific reasons for changing his mind about assuming the new responsibility or if it was entirely Musk's decision.

If Musk had joined the board, he would have been restricted to owning no more than 14.9% of the company's shares. However, now that he is no longer on the board, he has the freedom to increase his stake if he chooses. Some industry experts speculated on Twitter that he may attempt to take over the company.

Timeline of events

On Tuesday, Twitter's stock increased by 4% after the board made an announcement, finishing the day with a 2% gain. The previous day, following the revelation of Elon Musk's stake, Twitter experienced its best day since its IPO in 2013, surging over 27%.

Over the weekend, Musk shared several criticisms of Twitter and proposed changes to improve the social media platform and its offerings.

One suggestion was a crude joke in the form of a Twitter poll. Musk proposed that Twitter should change its name to "titter" by removing the "w," which is a reference to female anatomy.

Musk proposed more serious suggestions for Twitter Blue subscribers, including the option to pay with dogecoin, receive an "authentication" checkmark, and enjoy ad-free Twitter Blue.

""Twitter Blue subscribers should receive an authentication checkmark and no ads, as relying on advertising money for survival enhances corporations' power to dictate policy," Musk wrote."

"Since no one shows up, Musk advised Twitter to turn its headquarters office in San Francisco into a homeless shelter,".

He proposed that Twitter user numbers may be inflated by bots and at some point inquired about the platform's decline.

— Additional reporting by CNBC's Lora Kolodny.