Music manager Scooter Braun says his family received "numerous death threats" after Taylor Swift said he was stopping her from playing her old hits.
The star has been vocal in her disapproval of Braun since his company bought her back catalogue in June.
She accused him of "incessant bullying", and said he had tried to sabotage an award show appearance.
Braun had remained silent on the feud but said threats to his family had forced him to change his mind.
"I came home tonight to find my wife had received a phone call threatening the safety of our children" he wrote in an open letter to Swift, which appeared on his Instagram account.
The 38-year-old also posted a screenshot of a text he'd received saying: "Why don't you just die with your children? I will buy a gun [tomorrow] and then shoot you all in the head."
Addressing Swift, he said: "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.
"We are living in a time of pointless violence and as a husband and father I am concerned."
He called for the star to meet him and resolve their differences, while noting that his previous overtures towards Swift had all been rejected.
"Many have told me that a meeting will never happen as this is not about truth or resolution but instead a narrative for you. I am hopeful that is not the case," he said.
"I'm right here, ready to speak directly and respectfully. But if you would prefer to make large public statements while refusing to work towards resolving things amicably then I just pray that nobody gets seriously hurt in the process.
"I continue to wish you the best and hope we can resolve this."
Braun has two sons and a daughter, all under the age of four, with his wife, Yael Cohen.
The BBC has contacted Swift's representatives for a response.