Swift last week urged her 122 million Instagram fans to let Braun and Big Machine founder Scott Borchetta "know how you feel about this".
In an Instagram post addressed to Swift on Friday, Braun wrote that since Swift's statements "there have been numerous death threats against my family". He attached one threat made on Twitter.
He said he returned to his Los Angeles home on Thursday "to find my wife had received a phone call threatening the safety of our children".
"I assume this was not your intention but it is important that you understand that your words carry a tremendous amount of weight and that your message can be interpreted by some in different ways," Braun wrote.
Braun said after six months of fruitless attempts behind the scenes to mend their relationship, he felt he had no choice "than to publicly ask for us to come together and try to find a resolution. I have tried repeatedly through your representatives to achieve a solution but unfortunately here we are".
This is not the first time that Swift has hit out at Braun and Borchetta online.
In July 2019, Swift penned a Tumblr post calling out Borchetta for denying her the ability to own her master recordings without producing more albums for the label first.
The country-pop star also expressed that she was "sad" and "grossed out" to learn that her own music would be bought by none other than Braun of Ithaca Holdings, who had recently acquired Big Machine Records.
Taylor accused Braun of bullying her, along with Justin Bieber and Kanye West when Kim Kardashian leaked a recording of a phone call between Taylor and Kanye.
