Shultz, who held four Cabinet-level positions under two different presidents, was instrumental in helping to ease Cold War tensions between the U.S. and the Soviet Union.
His remarks come after a U.S. Defense Department test of a modified Navy Tomahawk cruise missile, and the demise of the Intermediate-Range Nuclear Forces Treaty between Washington and Moscow.
The Intermediate-Range Nuclear Forces Treaty was signed in 1987 by President Ronald Reagan and Soviet leader Mikhail Gorbachev. The U.S. has long accused Russia of refusing to comply with its terms.
The U.S. said last week it would stop abiding by the Cold War treaty banning intermediate-range nuclear missiles. "Our response will be symmetrical," Russian President Vladimir Putin said.
Secretary of State Mike Pompeo said the U.S. will suspend its obligations under the 1987 INF treaty as of Saturday and pull out in six months if Russia isn't deemed to be in compliance.
The national security adviser said the U.S. will leave the INF Treaty "in due course" — and that President Trump and Russian President Vladimir Putin would like to speak directly again next month.
Signed by Ronald Reagan and Mikhail Gorbachev in 1987, the Intermediate-Range Nuclear Forces Treaty eliminated an entire class of nuclear weapons. President Trump says he intends to withdraw.