An impasse between the U.S. and Iran shows no sign of thawing, with the two sides remaining at odds over the terms of ending their five-month war and giving conflicting messages on the Strait of Hormuz overnight.

Citing a source who holds a senior position in the Iranian government, Reuters reported on Wednesday that no breakthroughs had been made in efforts to revitalize an interim peace deal reached in June.

“One of the issues that is being discussed ⁠via mediators is the U.S. returning to the interim agreement and defining a timeframe for implementing its ​commitments. There has been absolutely no progress on this issue,” the individual told Reuters.

“There is no ​talk of an extension because … the United States violated the interim agreement 48 hours after it was reached ​and withdrew from it a few days later,” they said.

The interview came after a report from Turkey’s Andolu news agency stated the U.S. and Iran had agreed to extend a 60-day ceasefire, citing Pakistani government sources.

Both sides have accused each other of violating the terms of their Memorandum of Understanding since it was agreed, with U.S. President Donald Trump declaring the deal “over” at the NATO summit last month.

Warfare has continued in the Middle East in recent weeks, with U.S. forces launching a barrage of strikes on Iranian targets in retaliation for commercial ships in the Strait of Hormuz coming under attack, and deadly attacks on vessels in the Gulf of Oman and the Red Sea being reported this week.

Meanwhile, Iranian officials have disputed Trump’s repeated claims that Washington has “total control” over the Strait of Hormuz.

Iranian Foreign Minister Seyed Abbas Araghchi said in a post on X on Wednesday that the U.S. “has long miscalculated due to intelligence failures.”

“Case in point: The war on Iran. Now, an even bigger miscalculation on the Strait of Hormuz,” he said.

His comments came after Trump had said in a Truth Social post earlier that “the U.S.A. has total control over the Strait of Hormuz. I THINK WE WILL KEEP IT!” The president’s comments reiterated his assertion earlier this week that U.S. forces have “100% control” over the waterway, a critical route for international shipping.

Iran’s Persian Gulf Strait Authority said in a post on X, meanwhile, that “claims and repeated posts by U.S. officials that the Strait of Hormuz is no longer blocked do not change the reality: the Strait of Hormuz remains blocked and will not be reopened until Iran’s conditions are accepted.”

While both sides continue to make contradictory claims, data from trade intelligence firm Kpler showed that ship traffic through the Hormuz waterway is near a 3-month low.

Vessel transits sat at a 5-day average of around 13 on Tuesday, nearly the lowest level since May 12, according to a CNBC analysis of data provided by the trade intelligence firm Kpler. This includes ships of all types, from cargo vessels to oil tankers.

Traffic is about 90% lower than the daily average of 130 ships that transited Hormuz before the U.S. and Israel attacked Iran on Feb. 28.

Both Washington and Tehran have hardened their negotiating stances, asking for “reparations” from the other side, among other demands.

Iran’s Supreme National Security Council laid out sweeping demands over the weekend for reopening the Strait of Hormuz, including an end to the U.S. naval blockade, sanctions relief, American troop withdrawals and war reparations.

The developments come as Mohammad Reza Naqdi, a top advisor to the commander of Iran’s Islamic Revolutionary Guard Corps, told PBS in an interview on Tuesday stateside that “victory is on our side” and that “we have also seen how the American military is weaker than what we perceived.”

He pointed to what he described as Washington’s shifting objectives over the course of the conflict, including wanting to invade Kharg Island and opening the Strait of Hormuz.

“We saw confusion and bewilderment in America. It became a war without a strategy. Every two or three days, they announced a new objective … They mobilized their battleships. Everything they tried, we can show how we were victorious.”

When asked if the plan was to drag the conflict out until Trump leaves office, Naqdi said the goal was for Iran to “attain deterrence.”

As such, he said that one way was to prolong the conflict and cause attrition, so if anyone wants to attack Iran, there will be a cost.

— CNBC’s Spencer Kimball and Deena Zaidi contributed to this report.