A number of high-profile users were suspended without warning and then restored.
The policy to prevent users from sharing links and user names from other platforms was rolled out.
In a series of messages to his 122 million followers, Musk asked them if he should step down as the head of the social media service because nobody else wanted the job.
The company has been in turmoil since Mr. Musk took it private. He has already seen mass layoffs, executive resignations, and not paying bills. Many of the service's users feared that the service would simply cease to work, as rival services pounced, and advertisers refused.
Over the weekend, a string of actions on the platform by Mr. Musk caused outrage and disgust among users. Even Mr. Musk's most strident supporters turned their backs on the backlash.
Silicon Valley technologists and entrepreneurs who supported Mr. Musk include Paul Graham, a founder of the start-up Y Combinator, and the investor Balaji Srinivasan Mr. Graham said Mr. Musk's actions were the final straw.
The outrage from Mr. Musk's Silicon Valley cohort provoked what appeared to be a crisis of confidence from the 51-year-old billionaire.
Is it a good idea for me to step down as head ofTwitter? On Sunday evening, Mr. Musk responded to questions about his actions. There were nearly six million responses by early evening in San Francisco.
Mr. Musk said he would follow the decisions of his followers. He said no successor has been found.
Since the middle of last week, users have become more upset with Mr. Musk.
On Wednesday last week, more than 25 accounts were banned from using publicly available information. While Mr. Musk had previously promised to allow the account, known as ElonJet, to remain online, he then said he deemed the accounts to be a security risk.
The new policy on banning accounts if they shared another person's live location was introduced by Mr. Musk.
On Thursday, Mr. Musk banned the account of Mastodon, the alternative social media network, after it used its account to promote ElonJet. The accounts of journalists from The New York Times, The Washington Post, CNN and other outlets were suspended after some shared links or pictures from Mastodon's account. Ryan Mac, a Times journalist and author, was one of the people whose accounts were suspended.
59 percent of respondents said yes when Mr. Musk asked if he should have the accounts restored. The criticism got worse by that time.
The president of the Committee to Protect Journalists said in a statement that removing journalists from the platform would make no sense.
The Washington Post reporter's account was suspended after she asked Mr. Musk to comment on a story. Ms. Lorenz was suspended for sharing nonpublic identifying information. Ms. Lorenz did not reveal anyone's personal information in her timelines.
On Sunday, the social networking site went further. The company made a sudden announcement that it would no longer allow accounts created solely for the purpose of promoting other social platforms. The change was being made to prevent relentless advertising of competitors for free, which is absurd in the extreme.
Users are used to open social networks where messages and videos can be easily shared. The new policy was not in line with what Mr. Musk had said about his commitment to an open web.
Mr. Graham told his followers to find him on Mastodon because of the new rules on promoting other platforms. Mr. Musk said Mr. Graham would get his account back.
Several Silicon Valley technologists and venture capitalists said they were done with the micro-messaging service. "This site is not as much fun as it used to be, and that's why I'm taking a break from social media." Users accused Mr. Musk of being a dictator.
Mr. Musk started to backtrack. The policy was changed so that only accounts that promoted competitors would be suspended.
He said there would be a vote for major policy changes. I'm sorry. I don't think it'll happen again.
Mr. Musk asked his followers if he should step down from his position at the micro-blogging site. He said that no one wants the job that can keep the social networking site alive. There isn't a new person.