"We continually review the merits, both from the standpoint of diplomatic but also global consequences, of designating the Iranian Revolutionary Guard in its entirety as a terrorist organisation", Tillerson said.
Iran is a key ally of Russian Federation, the Iranian-backed Hezbollah movement of Lebanon, and the Syrian government of President Bashar al-Assad.
Senior Iranian officials, however, have pointed a finger at Saudi Arabia, Iran's Sunni regional rival.
But the missiles sent a message to more than just the extremists in Iraq and Syria, Sharif told state television in a telephone interview. While Iran has other ballistic missiles it says can reach longer distances, Sunday's strike appears to be the furthest carried out overseas.
The advances also opened the way for cooperation among Syrian, Iranian-backed fighters and the Iraq Popular Mobilization Units for any moves against Deir el-Zour.
Activists in Syria said they had no immediate information on damage or casualties from the strikes.
The Guard, which is also involved in the fight against the Islamic State group in neighboring Iraq, controls Iran's missile program.
The IRGC warned that these missile strikes were "just a warning to deter any further action by the terrorists", adding that ISIS' "regional and trans-regional supporters", possibly meaning Saudi Arabia and the United States, will be "engulfed by its [Iran's] revolutionary wrath and flames of the fire of its revenge in case they repeat any such devilish and dirty move in future".
It's also aimed to tell the us that Iran is fighting the Islamic State on its own terms, Handjani said.
The missile attack came amid recent confrontations in Syria between USA -backed forces and Iranian-backed pro-government factions.
"The three captured members of the Iranian Revolutionary Guard are now being questioned by Saudi authorities", it said, citing a Saudi official.
"We are following their actions".
"Firing these missiles from 600 or 700 kilometres away onto a small building. demonstrates Iran's capacity and intelligence capabilities" against jihadist groups, he said.
"The worst thing any of us could do right now is address this with hyperbole", Dunford said. "The supporters of terrorists should take heed of Iran's message of strength". It is still unclear what the missiles struck, and Iran has provided few details.