In New York to attend a UN forum on development, Zarif said he was open to speak with Tillerson as Washington carries out a review of the 2015 agreement reached with world powers on curbing Iran's nuclear program.
"There are no communications between myself and Secretary Tillerson," Zarif said at an event at the Council on Foreign Relations.
"It doesn't mean there can't be. The possibilities for engagement... Have always been open."
"We receive contradictory signals," Zarif said when asked about the possible outcome of the review.
"It's very clear that Iran is serious about the nuclear deal and we believe the nuclear deal can lay the foundation."
The absence of communication with the US administration is in sharp contrast with Zarif's dealings with former secretary of state John Kerry, with whom he negotiated the agreement.
Zarif said he and Kerry spent more time together "than with anybody else."
Representatives of the five nuclear powers -- China, Russia, France, Britain, the United States -- plus Germany are to meet in Vienna on Friday to take stock of the deal.
Zarif said they would discuss Iran's complaints about non-US compliance, accusing the US administration of failing to lift sanctions in line with the deal.
Any move by the US Congress to re-impose sanctions on Iran would "of course" be "a violation" of the nuclear deal, Zarif said, but he did not say what Tehran's response would be to such legislation.
Asked about Xiyue Wang, a 37-year-old researcher at Princeton University, Zarif said Iran's courts were independent and that "we in the government do not have any control over the decisions of the judiciary.
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