Egypt's interim government has praised the United States for showing "understanding" by describing the rule of ousted President Mohammed Mursi as undemocratic.

Foreign Ministry spokesman Badr Abdelatty said the US comments "reflect understanding and realisation ... about the political developments that Egypt is witnessing in the recent days".

He said it embodied "the will of the millions of Egyptians who took to the streets starting on June 30 to ask for their legitimate rights and call for early elections".

In an apparent reversal of US policy, State Department spokeswoman Jen Psaki said Mr Mursi's government "wasn't a democratic rule".

She added: "What I mean is what we've been referencing about the 22 million people who have been out there voicing their views and making clear that democracy is not just about simply winning the vote at the ballot box".

Earlier, Egypt accused Iran of "unacceptable interference" in its domestic affairs for having criticised the Egyptian army's removal of Mr Mursi.

The incident signalled a return to cooler relations between the two Middle Eastern powers after an attempt at rapprochement under Mr Mursi, who hails from the Islamist Muslim Brotherhood.

Iran on Monday called the ousting of Mr Mursi after mass protests against him a "cause for concern" and suggested that "foreign hands" were at work in the Arab state.

Egypt this morning expressed "extreme discontent" with the Islamic Republic's comments, saying they reflected a "lack of precise knowledge of the nature of the democratic developments Egypt is witnessing".

"This represents unacceptable interference in Egypt's internal affairs," the foreign ministry said in a statement on its Facebook page.

Egypt made similar remarks to Turkey after its Islamist government criticised Mr Mursi's overthrow.

Western states have been cautious so far in characterising the military overthrow of Mr Mursi.

The US has specifically avoided referring to it as a "coup", a word that would force it to halt aid including $1.3bn per year for the army.

Relations between Egypt and Iran broke down after the 1979 Iranian revolution, when Egypt gave sanctuary to the deposed shah.

Many Egyptians harbour strong feelings against Iran.

Mr Mursi tried to improve ties after he was elected in 2012.

Iranian President Mahmoud Ahmadinejad visited Cairo in February, the first visit by an Iranian leader in more than three decades.

But the two countries remained sharply divided on Syria. Shia Muslim Iran is the main backer of President Bashar al-Assad while Mr Mursi, often under pressure from hardline Sunni Muslim allies, backed Syria's largely Sunni rebels.

Egypt historically has much stronger ties to Gulf Arab states who have vied with Iran for regional influence.

Kuwait, Saudi Arabia and the United Arab Emirates provided Cairo's cash-strapped government with $12bn in aid this week.