Speaker Mohammad Bagher Qalibaf did not elaborate on how much uranium Iran planned to enrich.
The announcement comes after an attack this past weekend that damaged centrifuges, which is suspected of having been carried out by Israel.
The burning issue is that the US should come up with a concrete plan to lift sanctions, and based on this, Iran should comprehensively resume the implementation of the JCPOA, Wang Qun, Chinese envoy to the United Nations and other global organizations in Vienna, said at a meeting of the Joint Commission of the JCPOA in the Austrian capital.
The Joint Commission of the JCPOA resumed its talks on Thursday in Vienna, after a blackout struck the Natanz enrichment facility in central Iran on Sunday morning.
"I am proud to announce that at 00:40 last night, and on the night of the pilgrimage of Sayyid al-Shuhada, young and pious Iranian scientists were able to obtain a product of 60% enriched uranium".
He said the enrichment began just after midnight on Friday local time.
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Separately, two diplomats said Stoltenberg would chair a video conference with allied defence and foreign ministers on Wednesday. Underlying Tuesday's meeting is also Ukraine's wish to become a North Atlantic Treaty Organisation member.
The head of the Atomic Energy Organisation of Iran, the country's civilian nuclear arm, later acknowledged the move to 60 per cent, according to state TV.
Zarif's tweet followed a separate post he made a day earlier in which he warned that the recent act of "nuclear terrorism" at the Natanz enrichment facility had "unleashed [a] unsafe spiral that can only be contained by ending United States economic terrorism initiated by Trump".
The International Atomic Energy Agency, which monitors Iran's nuclear program, did not immediately respond to a request for comment. In January, Iran began enriching uranium from the 3.67 concentration allowed under the deal to 20 percent - a step closer to the 90 percent required for the fissile material in a nuclear weapon. Iran has continually denied it intends to assemble nuclear weapons.
He said Washington should lift all sanctions relating to the Iran nuclear issue - be it sanctions on Iran or long-arm jurisdiction measures on third-party entities and individuals.
Iran previously had said it could use uranium enriched up to 60 per cent for nuclear-powered ships. However, the Islamic Republic now has no such ships in its navy. Iranian Deputy Foreign Minister Seyed Abbas Araghchi, along with corresponding officials from Russia, Britain, France, Germany and China, attended the meeting.
His comments follow a report by Axios last week citing an unnamed senior Biden official, who said that the United States had "put forward some very serious ideas" and "demonstrated a seriousness of purpose" at the recent Vienna nuclear talks, while Iran has yet to demonstrate that it will "match" "that seriousness of objective".