US officials have agreed to donate four fighter jets to Egypt's army, in the latest indication of international support for the country's interim government despite growing internal unease at the new regime's management of the power transition.

America's donation of the F-16s suggests the Obama administration is coming to terms with the downfall of the former president Mohamed Morsi, after initially displaying an ambiguous attitude to the military's role in the Islamist's ouster. The US gives annual aid worth $1.3bn (£860m) to the Egyptian army. There were concerns in Egypt that this support might be discontinued in the aftermath of Morsi's departure.

The aircraft donation follows a telephone conversation between the European Union's foreign affairs representative, Lady Catherine Ashton, and Egypt's new interim president, Adly Mansour. It follows the issuing of $12bn in grants and loans from Saudi Arabia, the United Arab Emirates and Kuwait, all conservative Gulf states known for their opposition to Morsi and his Muslim Brotherhood.

It also comes as both Egypt's main secular opposition group and the grassroots movement that prompted last week's military intervention expressed concern over the manner in which the new regime has handled the first days of the post-Morsi era.

The Muslim Brotherhood has continued to refuse to engage with the Mansour-led regime, calling for a mass march on Friday in support of Morsi.

The Tamarod campaign – which brought millions on to the streets on 30 June in protests that led the army to oust Morsi – raised doubts over Egypt's new constitutional declaration, announced on Monday, which will act as a blueprint for Egypt's leaders until a more permanent charter is written.

"We were not consulted on the constitutional declaration and we will submit our amendments to it," a Tamarod spokesman, Hassan Shaheen, wrote on social media.

Among several concerns, the declaration has been criticised for giving both executive and legislative power to Mansour.

The National Salvation Front, the formal secular coalition that had led the opposition to Morsi before Tamarod's emergence, said: "The declaration includes articles that we do not accept, others that need to be amended, and that new articles need to be added". The NSF spokesman Khaled Daoud said Egypt's government should be formed from those who played a key role in the 2011 revolution that toppled Hosni Mubarak.

The NSF statement reflects wider concerns that Morsi's departure – painted by many as a return to the values of the 2011 revolution that ousted Mubarak – instead runs the risk of rehabilitating figures and institutions once closely aligned to the latter's regime.

The police force is one. Their brutality was a major cause of the 2011 revolution, and their reform was one of the revoluntionaries' implicit demands. But the obvious enthusiasm of the police for Morsi's fall has helped to rehabilitate them in the eyes of some. Uniformed officers were seen with anti-Morsi propaganda in the run up to his departure, while police failed to protect the offices of his political allies. Many officers even marched against Morsi, and at some such rallies, protesters chanted: "The police and the people are one hand".

Many Egyptians are offended by the idea that Morsi's removal was a coup not a revolution. But others have suggested that it was at least partly facilitated by Mubarak-era figures, riding the wave of popular dissent against his regime. Morsi's last supply minister, Bassem Ouda, told the Guardian that the extreme, countrywide petrol shortage – which cemented anti-Morsi fury in the week that led to his departure – was aided by interior ministry officials seeking his ouster.

According to Ouda's allegations, Mubarak holdovers in the interior ministry seeking to foment anti-Morsi anger paid thugs "to take over a lot of gas stations in the provinces, and to stop the gas stations from selling products – or to sell it at double its market price".

Continued petrol queues across parts of Egypt appeared to contradict Ouda's narrative. And Cairo petrol station officials said that while last week's extreme shortage may not have been created by Morsi, it was not necessarily the result of sabotage.

"The problem happened in the main storage facility where the fuel first arrives [from abroad]," said Ihab Kamel, a petrol station manager in central Cairo. "The facility wasn't working properly on one day and because of that, coupled with the approach of 30 June, people started to panic and started to fill up their tanks whether or not they were empty. Normally people fill their tanks up every three days – but last week they were filling up, going home, siphoning the petrol into separate containers, and then coming back for more."

But while allegations that government departments helped to facilitate Morsi's departure remain unproved, there are signs that some in government are at least now more willing to do their jobs. Some of the walls that blocked whole streets in central Cairo under Morsi have suddenly been removed. A few blocks away, just hours after Morsi's removal, government officials painted new street markings – while shoppers on the eve of Ramadan commented that police were finally back on the streets after their disappearance as the crisis peaked 10 days ago.

But there is little sense that the country's economic plight is about to improve suddenly.

This week's input of $12bn from the Gulf is intended to boost Egypt's badly depleted foreign currency reserves. Any new government will eventually have to tackle the question of expensive subsidies of food and fuel as the price of negotiating a loan from the International Monetary Fund.