Murray earned his first cap in a 5–0 defeat against England in Los Angeles, on June 16, 1985, while still in college. His first national team goal came against Uruguay on February 7, 1986. The game ended in a 1–1 tie. Murray went on to play on the U.S. team at the 1988 Summer Olympics, and become a mainstay in the lineup during World Cup qualifying. Murray started all three games for the US at the 1990 FIFA World Cup, the U.S.'s first appearance at the Cup since 1950. His play in the World Cup saw him having a hand in both goals scored during the finals, scoring one and assisting on the other.