The tweet, which he later deleted, linked to an article by the Santa Monica Observer, an outlet that previously said Hillary Clinton died on 11 September and was replaced with a body double.
Police in San Francisco have said the suspect in last week's attack, identified as David DePape, 42, broke into the Pelosi family's Pacific Heights home early on Friday and confronted Mr Pelosi, demanding to know,"Where is Nancy?"
The two men struggled over a hammer before officers responding to a 911 call to the home saw DePape strike Mr Pelosi at least once, police said.DePape was arrested on suspicion of attempted murder, elder abuse and burglary. Prosecutors plan to file charges on Monday and expect his arraignment on Tuesday.
Police say the attack was"intentional" and not random but have not stated publicly what they consider to be the motive. The exchange between Musk and Mrs Clinton came a day after Yoel Roth, Twitter's head of safety and integrity, said the company's policies toward"slurs" and"hateful conduct" were still in place.
Shortly after Musk took control of Twitter, some accounts on the platform began tweeting messages ranging from racist slurs to political misinformation, such as"Trump won", to see what will be tolerated.Mr Musk said on Friday that he would form a"content moderation council" and promised advertisers the site would not devolve into a"free for all hellscape".