At issue is heavy water, which is used to cool reactors that can produce substantial amounts of plutonium. That, in turn, can be applied to making the fissile core of nuclear warheads.
A recent report from the UN's International Atomic Energy Agency said that Tehran had more heavy water in storage than called for by the agreement between it and six world powers.
US diplomats have criticized the violation and with the incoming U.S. Administration warning it could try to overturn the deal, Iran's repeated breach of its commitment is adding concerns about its durability.
Iran has recently pledged to ship out five tons of the material to return to compliance, and the two diplomats said it had begun to do so over the past few days. They said the shipments were going to Oman, an Iranian ally.
In February, a month after the deal went into effect, the agency noted for the first time that Iran had exceeded its allotted limit of heavy water.
The amount was greater in that case and some of the excess was exported to the US under an arrangement criticized by US congressional opponents as facilitating Iranian violations of the deal.