Brzezinski said she asked Trump to explain his position on nuclear arms in an off-air conversation earlier that morning. Co-host Joe Scarborough called the president-elect's response "not quite the clarification that we would expect."
Trump allegedly told Brzezinski, "Let it be an arms race. We will outmatch them at every pass. And outlast them all."
Jason Miller, the incoming White House communications director, said in a statement Thursday that Trump's controversial tweet was simply addressing "the need to improve and modernize our deterrent capability as a vital way to pursue peace through strength."
But Trump's reckless comments have drawn concerns from several nuclear weapons experts.
Kingston Reif, director of disarmament and threat reduction policy for the Arms Control Association, called Thursday's tweet a "very bad sign."
"Even before these recent statements, the path we have been on is reckless and ill-advised and in need of a major course correction," Reif told The Huffington Post on Thursday. "Pouring more gasoline on the fire is exactly the opposite of what is needed."