The June interim ceasefire agreement set a 60-day period, extendable by mutual consent, within which Iran and the U.S. were expected to reach a final deal limiting Tehran's nuclear programme and lifting U.S. sanctions.
The Iranian source dismissed a report on Wednesday from Turkey's Anadolu news agency that quoted Pakistani government sources as saying they had agreed to extend that 60-day period.
"There is no talk of an extension because, from Iran’s perspective, there is no period that began and therefore nothing to extend. The United States violated the interim agreement 48 hours after it was reached and withdrew from it a few days later," the source told Reuters.
Both Iran and the United States have stepped up rhetoric in the past two days.
Iran's top security official, Mohsen Rezaei, said on Tuesday that the Strait of Hormuz would remain closed unless the U.S. accepted Iran's conditions to end the war.
That followed a new demand from Trump on Monday that Iran should pay compensation for people killed in 50 years of wars, attacks and protests.
Throughout the conflict, Trump has alternated between threats of escalation and claims that a peace deal is imminent.
Speaking to reporters after a visit to Ohio on Tuesday, Trump said: "Iran is going fine, going just absolutely fine."
"We have a country that has been the bully of the Middle East for 50 years, really 51 if you think about it ... and they're no longer the bully of the Middle East."
The Strait of Hormuz, a narrow waterway between Iran and Oman and the entrance to the Gulf, handled a fifth of global oil and liquefied natural gas flow before the war.
Benchmark Brent crude futures have surged since the start of the war in February, hitting a peak of $126 a barrel, roughly 75% above pre-war levels, with choppy trade reflecting concerns over disruptions to Gulf oil supplies and shifting signals on peace talks.
Those concerns were compounded by separate attacks on shipping on Tuesday.
At the southern end of the Red Sea, four crew members were killed in an attack by Iran-backed Houthis on a small cargo ship in the Bab el-Mandeb Strait on Tuesday, the first deadly strike on shipping by the group since the start of the war.
The U.S. military, meanwhile, said a U.S. Navy MH-60 helicopter fired two Hellfire missiles to disable the steering gear of a Panama-flagged cargo ship.
The ship ignored repeated warnings to stop violating a naval blockade on Iranian ports, the U.S. Central Command said. Maritime sources told Reuters the vessel was hit off Pakistan while sailing into the Gulf of Oman.
Brent futures rose 35 cents, or 0.4%, to $89.26 a barrel on Wednesday, heading for a sixth day of gains.
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