WASHINGTON — Tensions between the United States and Iran flared on Monday as Tehran said it would soon breach a key element of the 2015 international pact limiting its nuclear program, while President Trump ordered another 1,000 troops to the Middle East and vowed again that Iran would not be allowed to develop a nuclear weapon.

The Pentagon’s announcement of the troop deployment came three days after attacks on two oil tankers in the Gulf of Oman that the administration has blamed Iran for. And it came hours after Iran said it was within days of violating a central element of the landmark 2015 agreement — intended to curb its ability to develop a nuclear weapon — unless European nations agreed to help it blunt crippling American economic sanctions.

Iran’s Atomic Energy Organization said that within 10 days the country will have produced and kept in its stockpiles more low-enriched uranium — the sort used to fuel power plants — than allowed by the 2015 containment deal. The agency also left open the possibility that it might soon begin enriching the uranium to higher levels of purity, edging it closer to what would be necessary to build a nuclear weapon.

Mr. Trump pulled out of the 2015 pact last year, saying that it was not tough enough on Iran. In doing so, he put intense strain on the international coalition that had backed the agreement and wanted to keep it alive. And he left Iran trapped between continuing to abide by the deal’s provisions without getting any of its benefits or abandoning it and provoking a more intense conflict with the United States.