"We have agreed in the past, that is we and the Russian Federation pro-regime forces, that operations that the coalition were conducting in Syria were effectively degrading ISIS capability, and will work to restore that de-confliction chain in the next few hours", Dunford said.
"We follow their actions and we follow their words", he said Monday.
Israel, which is itself believed to have atomic weapons, says the programme aims to produce a nuclear bomb - something Iran denies.
While the Revolutionary Guard in Tehran boasted that the seven missiles overflew Iraq on their way to hitting an Islamic State command center and suicide vehicle bomb operation in Deir el-Zour, Israeli observers called the launchings a "flop".
The attacks marked the first time that ISIS, a Sunni Muslim group fighting Iranian-backed militias in Syria, has claimed responsibility for an attack in Iran.
Iranian military officials have separately vowed to use ballistic missiles and other armaments, including weaponized drones, to confront USA -backed forces operating in Syria.
Gen. Ramezan Sharif, head of the IRGC Public Relations Department, told Tasnim news agency that the IRGC fired six mid-range ballistic missiles at multiple targets, within a range of 650 to 700 km.More news: North Korea conducts rocket engine test
"We continually review the merits, both from the standpoint of diplomatic but also worldwide consequences, of designating the Iranian Revolutionary Guard in its entirety as a terrorist organisation", Tillerson said. The missiles flew over Iraq before striking eastern Syria.
Currently, Washington has only blacklisted the Guards' foreign operations arm - the Quds Force - and some individual commanders.
"Those who have done wrong will find out what they have coming to them", Qasem Soleimani wrote.
The Iranian government said it notified Damascus before it fired rockets into the country, but that it "will not be tied to formalities when defending its security and stability".
Russian Federation reacted angrily to the USA shootdown of the Syrian jet, which the Pentagon said was dropping bombs near the US -backed Syrian Democratic Forces, a mixed Kurdish-Arab militia fighting Islamic State.
Iran has been a major military backer of the Syrian regime, first in its war with rebel groups across the country and later against IS. Soleimani has been pictured on a number of occasions on the front lines in Syria.
United States officials insist they shot the Syrian warplane in "self defence" because coalition-backed fighters were threatened.
The presence of Iranian-backed troops, artillery and tanks and USA -led coalition forces in southern Syria, namely around the at-Tanf crossing at the Iraq-Syria border, has slowly turned the area into a flash point.