"He cancelled his trip due to unforeseen commitments that are requiring him to stay here in DC," Sims said.
The spokeswoman did not specify what commitments prompted Dunford to call off the trip.
US-Iranian tensions first flared up last year when the United States unilaterally withdrew from the 2015 nuclear agreement with Iran and started reinstating sanctions against Tehran. On May 8, Iran announced its decision to partially discontinue its obligations under the nuclear agreement.
On May 5, National Security Advisor John Bolton announced that the US had stepped up its military forces in the Middle East to send a "clear and unmistakable" message to Iran.
The enhanced deployment includes an aircraft carrier strike group, Patriot missiles, B-52 bombers and F-15 fighters, according to the Pentagon. Iranian Supreme Leader Ayatollah Ali Khamenei has said that Iran does not intend to wage war with the United States but will continue to resist Washington.