says: "I already know where you live. I'm on you."
A spokesman for Mr Kasowitz confirmed the authenticity of the emails and says Mr Kasowitz "intends to apologise" to the man.
Spokesman Mike Sitrick added that the missives were sent at the end of a "very long day."
"The person sending that email is entitled to his opinion and I should not have responded in that inappropriate manner," Mr Kasowitz said in the statement. "I intend to send him an email stating just that. This is one of those times where one wishes he could reverse the clock, but of course I can't."
On Tuesday, ProPublica published a story examining Mr Kasowitz's lack of security clearance and past behaviour at his law firm.
Mr Trump's longtime personal lawyer, Mr Kasowitz leads the outside legal team handling the president's response to investigations led by special counsel Robert Mueller and congressional committees looking into Russia's meddling in the election and any potential co-ordination with Trump associates.
Mr Kasowitz is well-known in New York business and real estate circles for his rough-and-tumble courtroom demeanour, though he has little criminal defence experience or expertise in navigating politically charged Washington investigations.
Last month, he entered the Russia investigation fray as the public face of Mr Trump's rebuttal to former FBI Director James Comey's testimony before the Senate intelligence committee.
Mr Comey testified that he believed he was fired because of the FBI's Russia investigation.
The White House referred questions about the emails to Mr Kasowitz and his legal team.
-AP, News Corp Australia Network