The comments were a further blow to hopes of a swift resolution to the crisis, following attacks on shipping in the region on Tuesday that pushed oil prices higher.
The comments on Wednesday came as US President Donald Trump issued yet another broadside against Iran's leaders, dealing a further blow to hopes for a resolution to the crisis.
The deal agreed to in June declared an "immediate and permanent termination of military operations on all fronts", but quickly unravelled, with Trump saying it was "over" on July 7 and Iran's foreign ministry declaring it "suspended" a week later.
Trump on Wednesday said the US has "total control" over the Strait of Hormuz. But the Persian Gulf Strait Authority, the body Iran set up to manage the waterway, said it remains blocked and would not be reopened until Iran's conditions are accepted.
"Iran is all talk and no action, the Bully of the Middle East No Longer," Trump said on Truth Social.
Throughout the conflict, he has alternated between threats of escalation and claims that a peace deal is imminent.
The US accuses Iran of failing to honour an agreement under the deal to reopen the vital Strait of Hormuz shipping route.
Iran says the US has reneged on its commitments, including lifting a blockade of Iranian ports and releasing frozen Iranian assets.
"One of the issues that is being discussed via mediators is the US returning to the interim agreement and defining a time-frame for implementing the commitments. There has been absolutely no progress on this issue," the Iranian source said.
There was no immediate comment from the US.
Thousands of people have been killed in the conflict, mainly in Iran and Lebanon, since the US and Israel launched attacks on Iran on February 28.
Iran has struck US assets and infrastructure in countries including Oman, Jordan, Kuwait, Israel, the United Arab Emirates and Saudi Arabia.
The June interim ceasefire agreement set a 60-day period, extendable by mutual consent, within which Iran and the US were expected to reach a final deal limiting Iran's nuclear program and lifting US 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.
Both Iran and the United States have stepped up rhetoric in the past two days.
Iranian top security official Mohsen Rezaei on Tuesday said the Strait of Hormuz would remain closed unless the US accepted Iran's conditions to end the war.
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 one-fifth of global oil and liquefied natural gas flow before the war.
At the southern end of the Red Sea on Tuesday, four crew members were killed in an attack by Iran-aligned 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 US military, meanwhile, said a US navy MH-60 helicopter fired two Hellfire missiles to disable the steering gear of a Panama-flagged cargo ship.
