"As we announced when we said our steps would continue, the stockpile has passed 300 kg," one of the sources said.
The semi-official Fars news agency quoted a source as saying that the United Nations' International Atomic Energy Agency (IAEA) had measured the stockpile on Monday. The IAEA was not immediately available for comment.
Enriching uranium to a low level of 3.6% fissile material is the first step in a process that could eventually allow Iran to amass enough highly enriched uranium to build a nuclear warhead.
Last Wednesday, the IAEA verified that Iran had roughly 200 kg of low-enriched uranium, just below the deal's 202.8 kg limit, three diplomats who follow the agency's work told Reuters. On Monday, the IAEA was not immediately available for comment.
After talks on Friday in Vienna, Iran said European countries had offered too little in the way of trade assistance to persuade it to back off from its plan to breach the limit, a riposte to U.S. President Donald Trump's decision last year to quit the deal and reimpose economic sanctions.
The deal between Iran and six world powers lifted most international sanctions against Iran in return for restrictions on its nuclear work aimed at extending the time Iran would need to produce a nuclear bomb, if it chose to, from roughly two to three months to a year.
Iran says its nuclear program is solely for peaceful purposes, including generating power.
In May, Washington piled pressure on Tehran by ordering all countries to halt imports of Iranian oil, and tensions have been growing in the Gulf ever since.
Washington has dispatched extra forces to the Middle East, and U.S. fighter jets came within minutes of conducting air strikes on Iran last month after Tehran downed an unmanned American drone.
In a speech on Monday broadcast live on state TV, Iranian Foreign Minister Mohammad Javad Zarif said: "Iran will never yield to pressure from the United States ... If they want to talk to Iran, they should show respect ...
"Never threaten an Iranian ... Iran has always resisted pressure and has responded with respect when respected."
Trump has called for negotiations with Iran with "no preconditions", but Tehran has ruled out talks until the United States returns to the nuclear pact and drops its sanctions.