Given the rapid Israeli advances following their strike on Egypt, the administration "thought the situation was so tense in Israel that perhaps the Syrians, fearing Israel would attack them, or the Soviets supporting the Syrians might wish to redress the balance of power and might attack Israel". The Soviets learned of this course correction and regarded it as an offensive move. In a hotline message from Moscow, Soviet Premier Alexei Kosygin said, "If you want war you're going to get war."[258]
The Soviet Union supported its Arab allies.[259] In May 1967, the Soviets started a surge deployment of their naval forces into the East Mediterranean. Early in the crisis they began to shadow the U.S. and British carriers with destroyers and intelligence collecting vessels. The Soviet naval squadron in the Mediterranean was sufficiently strong to act as a major restraint on the U.S. Navy.[260] In a 1983 interview with The Boston Globe, McNamara claimed that "We damn near had war". He said Kosygin was angry that "we had turned around a carrier in the Mediterranean".