The Iranian flag flutters in front the International Atomic Energy Agency (IAEA) headquarters in Vienna, Austria March 4, 2019.
The US has also blamed Iran for last week's attacks on two tankers in the Gulf of Oman, a charge Tehran has denied as "baseless".
The Atomic Energy Organization of Iran (AEOI) announced on Monday that Iran's stockpile of enriched uranium will exceed 300 kilograms by June 27.
In a news conference, Iranian atomic agency spokesman Behrouz Kamalvandi said that his country was increasing its production of uranium.
The secretary of Iran's Supreme National Security Council, Ali Shamkhani, said Tehran was responsible for security in the Gulf and urged USA forces to leave the region, state TV said.
He also said Iran would continue to allow the U.N.to inspect its nuclear facilities for the time being.
According to the Washington Post, Iran in May threatened to breach the 300kg uranium limit unless the remaining countries in the deal gave it economic concessions, giving them a 60-day deadline.
The nuclear deal had limited Iran to enriching uranium only to 3.67%, which is enough for power plants and peaceful purposes.
Tensions are now high between the USA and Iran after unexplained attacks on two oil tankers off the Iranian coast on Thursday. (Iran's counterpart to Instex is also under threat of sanction, of course.) That's a threshold gut-check question for Trump and Congress: Are they inclined to look the other way at Instex if it begins trading with Iran? Iran denies having any role.
The U.S. alleges Iran used limpet mines to target the tankers last Thursday, pointing to black-and-white footage it captured that American officials describe as an Iranian Revolutionary Guard vessel removing an unexploded mine from the Japanese-operated tanker Kokuka Courageous, one of the two ships that were targeted.
Representatives for the White House and the U.S. State Department did not immediately respond to a request for comment on the Iranian announcement.
"We are going to work to build out a set of countries that have deep vested interest in keeping (the Strait of Hormuz) open, to help us do that", he said.
"Should Iran deliver on its threats, the worldwide community will have to implement, immediately, the pre-set sanctions mechanism", he said on Monday.
The decision to increase uranium production is part of Iran's measures to reduce commitments to the JCPOA following the US' unilateral withdrawal from the agreement previous year, and the EU's failure to safeguard Iran's economic interests in the face of U.S. sanctions.
German Foreign Minister Heiko Maas rejected the Iranian ultimatum and insisted Tehran must stick to its commitments under the deal.
Kamalvandi accused Europeans of "killing time" as the clock runs down.
In an indication of concern at Iran's announcement, Germany urged Tehran to meet all its obligations under the 2015 accord.
File photo of the reactor building at the Bushehr nuclear power plant in southern Iran, 1200km south of Tehran.
Authorities are still debating whether to "redesign or revive" the Arak reactor, he added. "Iran had purchased pipes for replacement in case the West violated the deal".
But after America pulled out of the nuclear accord and escalated sanctions, Rouhani set a July 7 deadline for Europe to come up with better terms for the deal or Tehran would boost enrichment further.