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5 year oldIts atomic energy agency said it had quadrupled production of the material, which is used to make reactor fuel and potentially nuclear weapons.
But it added there was "still time" for European countries to act by protecting Iran from reinstated US sanctions.
The UK, France and Germany have warned Iran not to violate the deal.
They have previously said they will have no choice but to reimpose their own sanctions, which were lifted in return for limits on the Iranian nuclear programme.
Reuters news agency quoted a US National Security Council spokesman as saying the enrichment plans were "nuclear blackmail" and should be met with "increased international pressure".
"Iran's enrichment plans are only possible because the horrible nuclear deal left their capabilities intact," Garrett Marquis said.
"President Trump has made it clear that he will never allow Iran to develop nuclear weapons."
This latest development comes at a time of high tension in the Middle East, with the US accusing Iran of being behind suspected attacks that left two oil tankers ablaze in the Gulf of Oman on Thursday. Iran has denied any involvement.
Context in international affairs is everything.
In early May, Iran signalled its intention to break out from some of the constraints imposed by the nuclear deal. On Monday, it repeated that threat, adding that the rate of enrichment was being stepped up and that it expected to break the limit on the amount of low-enriched uranium it can hold before the end of this month.
But since its first announcement, the context has changed dramatically with two sets of attacks on oil tankers in the Gulf - both attributed by the US to Iran.
Many fear that Washington and Tehran are on the verge of a military clash and that miscalculation could tip them over the edge.
Iran's further threat today to increase its level of enrichment to a stage that would bring it much closer to "weapons-grade" material adds another element of risk into an already combustible mix.
Enriched uranium is produced by feeding uranium hexafluoride gas into centrifuges to separate out the most fissile isotope, U-235.
Under the nuclear deal, Iran is only permitted to produce low-enriched uranium, which has a 3-4% concentration of U-235 and can be used to produce fuel for nuclear power plants. "Weapons-grade" uranium is 90% enriched or more.
Iran has complained that European powers have failed to abide by their commitments to mitigate the effects on its economy of the sanctions that US President Donald Trump reinstated after abandoning the nuclear deal last year.
Mr Trump wants to force Iran to renegotiate the accord and agree to curb its ballistic missile programme and end its "malign" activities in the Middle East.
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