WASHINGTON (AFP) - The military toppling of Egypt's Mohamed Mursi could have huge implications for key ties with the United States (US), which had an uneasy relationship with his Islamist-led government during its year-long rule.

Analysts and lawmakers have for months sharply criticised the tepid US response to Mr Mursi's failure to usher in a more inclusive government to meet the demands of the hundreds of thousands of Egyptians who have taken to the streets.

"In what has to be one of the most stunning diplomatic failures in recent memory, the United States is - in both perception and reality - entrenched as the partner of a repressive, Islamist regime and the enemy of the secular, pro-democracy opposition," wrote Republican senator Ted Cruz in Foreign Policy magazine on Wednesday.

Time and again in recent months, Washington has failed to articulate a strong response to controversial moves by Mr Mursi to consolidate power and his reluctance to introduce much-needed economic reforms, content to observe that democracy takes time.

After days of unrest and only hours before Mr Mursi was ousted, State Department spokesman Jen Psaki on Wednesday finally spoke out to criticise Mr Mursi, saying he needed to do more to address the Egyptian people's concerns.

In a telling sign, she also refused to take issue with the military, or to say whether an army takeover would amount to a coup, repeatedly stressing that "we don't take sides, as you know".

In the immediate aftermath of Mr Mursi's ouster, US officials remained silent, as emergency talks were being held at the White House. The State Department, however, ordered the mandatory evacuation of its Cairo embassy.

From the beginning of Mursi's rule in June 2012, Washington has sought to cajole him into meeting the huge expectations that his election would mark the dawning of a more democratic era.

In a show of support for Egypt, then US Secretary of State Hillary Clinton toured the emblematic Tahrir Square in March 2011 following the overthrow of Mr Hosni Mubarak's 30-year-old regime.

She travelled back to Cairo last year to meet with Mr Mursi just days after his election.

But she was met by booing crowds and pelted with eggs and tomatoes by Egyptians incensed that Washington was backing a known Islamist leader and allowing the promise of the revolution to slip away.

With things spiralling out of control, President Barack Obama in September inadvertently hinted at US frustration, saying in a television interview of the Islamist government that "I don't think that we would consider them an ally, but we don't consider them an enemy".

Yet the Egyptian military's ousting of the country's first ever democratically elected president presents Washington with an uncomfortable dilemma, and could have wider implications for the US$1.3 billion (S$1.7 billion) in annual military aid it lavishes on Egypt.

Under US law, Washington may have to suspend that military aid as well as millions more in economic assistance.

While what happened in Egypt "may technically be a coup d'etat" it should not necessarily be seen as an "interruption of Egypt's democratic development," said Mr Brian Dooley, from Human Rights First.

Mr Mursi had already taken the "country in an anti-democratic direction," he argued, adding that the events should be seen as a wake-up call to Washington.

Many Egyptians have welcomed the military's intervention and believe the army - largely trained and equipped by the US - will work to preserve the country's new-found democracy.

Indeed, new US Secretary of State John Kerry earlier this year praised the military for helping to prevent a civil war in the 2011 uprising, even though they took some time afterward to step aside.

"I think the military has been the best investment that America has made in years in that region," Mr Kerry told the Senate Foreign Relations Committee in April.

"The army in Egypt has been, frankly, an incredibly responsible player in this drama. But for the army, you would have had a civil war, I think, in Egypt. You would have had massive bloodshed."

A new fully functioning government in Cairo would also be a huge relief to Washington as it seeks progress on other global issues including the Middle East peace process and the Syrian conflict.

A top Arab official told reporters in Washington this week that Egypt's neighbours might not be against a military takeover, providing it led to a stable and secure country, lamenting that for months the crisis-hit country had been unable to act as a leading regional player.