Three days after buying the social networking site, Musk posted a false allegation about the attack on the husband of the speaker.
The question of how Mr. Musk will fight misinformation and hate speech on social media was raised again.
Hillary Clinton, the former first lady and 2016 Democratic presidential nominee, accused Republicans of spreading "hate and deranged conspiracy theories" that she said had helped the man who attacked Ms. Pelosi.
Mr Musk shared a link to an article in the Santa Monica Observer after he replied to Mrs. Clinton. According to the article, Mr. Pelosi was drunk and in a fight with a man.
The Santa Monica Observer is notorious for publishing false news according to an editorial in The Los Angeles Times. The publication claimed that Mrs. Clinton had died and that a body double was sent to debate Donald J. Trump.
According to the police, Mr. Pelosi was attacked with a hammer by a man who had entered through the back door. Two men were wrestling for control of a hammer when the police arrived at the home. The authorities said that Mr. DePape would likely be charged with attempted Homicide and assault with a deadly weapon. The man is said to have shouted, "Where is Nancy?" Nancy is not located.
On Saturday, Mr. Musk wrote an open letter to advertisers saying that he would not allow unfettered commentary on the site.
Anything that can be said with no consequences can become a free-for-all hellscape. They want to be the most respected advertising platform in the world.
On the same day that he fired several of the company's top leaders, Mr. Musk completed his purchase of the social networking site.
Ahead of the chance of sweeping changes at the platform, like reinstating the account of Mr. Trump, Mr. Musk has said he would create a content moderation council.
There will be no major decisions before the council convenes.