The six-month agreement only provides for the easing of limited sanctions and the unblocking of some frozen Iranian assets abroad and foreign firms should not "over-interpret" its scope, the official said.
"Businesses need to take into account the legal and reputational risk of doing business with Iran", he said, speaking on condition of anonymity.
The official added that Italy had been identified by Washington as one of the countries with historic and current trade ties with Iran and pointed out that Tehran saw Italy as a possible "gateway" to Europe.
Italian oil major ENI, along with other foreign oil firms, should "convey to their partners in the oil sector that they are not going in now," he said.
The US is engaged in "an ongoing effort to visit key partners to continue to ensure that the sanctions regime that has been built over the past 5-10 years remains robust, remains in place," he said.
The international deal with Iran is due to come into force from January 20th and foresees the suspension of certain sanctions on gold and precious metals, Iran's auto sector, and petrochemical exports.
It will also allow for safety-related repairs and inspections for some Iranian airlines, ease restrictions on oil shipping and unblock €3.1 billion from sanctioned Iranian oil sales.