Kerry made the controversial remarks at a closed-door meeting of the influential Trilateral Commission on Friday, the news website reported on Sunday.
According to the website, a source at the gathering provided them with a recording of Kerry's remarks.
"A two-state solution will be clearly underscored as the only real alternative. Because a unitary state winds up either being an apartheid state with second class citizens -- or it ends up being a state that destroys the capacity of Israel to be a Jewish state," Kerry said, according to a new website.

"Once you put that frame in your mind, that reality, which is the bottom line, you understand how imperative it is to get to the two state solution, which both leaders, even (Thursday), said they remain deeply committed to," he reportedly said.
The online publication said that US, Western European, Russian, and Japanese senior officials and experts were at the event.
The term "apartheid" is a reference to South Africa's 1948-1994 oppressive and racially segregated social system.
While both Kerry and President Barack Obama have refrained from using the term when speaking of the Israeli-Palestinian conflict, former president Jimmy Carter (1977-1981) titled a 2006 book that he wrote on the subject "Palestine: Peace Not Apartheid."
Kerry also insisted that the peace process was not dead.
"The reports of the demise of the peace process have consistently been misunderstood and misreported. And even we are now getting to the moment of obvious confrontation and hiatus, but I would far from declare it dead," Kerry said, according to the news website.


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