* EU's Ashton in Cairo to push reconciliation
* Thousands of Brotherhood supporters in streets
* Army attacked near Gaza
Thousands of supporters of deposed Egyptian President Mohamed Mursi demonstrated outside the prime minister's office on Wednesday in a "day of steadfastness" to protest against the formation of a new interim cabinet on its first day on the job.
Protesters held up Korans and portraits of Mursi in the blistering noon heat outside the main government buildings in the centre of Cairo, demanding Mursi be restored to power. They shouted "God is Greatest!" and "Down with military rule!"
"We have only two goals, legitimacy or martyrdom," said Ahmed Ouda, 27. Another man interrupted to add: "Peaceful martyrdom!"
Crisis in Egypt, which straddles the Suez Canal and has a peace treaty with Israel, has alarmed its allies in the West and the region. Catherine Ashton, the European Union's foreign policy chief, is due in town, the latest international figure to meet Egypt's interim rulers.
Unlike a U.S. envoy who came two days ago, she is also expected to meet senior figures in Mursi's Muslim Brotherhood.
The army, which removed Egypt's first freely elected president from power two weeks ago, accused Mursi's supporters of inciting armed demonstrations near military bases and trying to turn a political dispute into a religious quarrel.
Egypt swore in an interim cabinet on Tuesday of 33 ministers, mostly technocrats and liberals. Not one was drawn from the two main Islamist factions that won five straight elections since a 2011 uprising toppled autocrat Hosni Mubarak.
"Does it believe in itself? Does anybody?" Essam El-Erian, a senior leader in Mursi's Muslim Brotherhood, said on Facebook of the new cabinet. "How can it have any authority when it knows that with one word from the military all its members can be sent home on pain of being arrested?"
The swearing-in took place in an ornate hall hours after overnight street battles between Mursi supporters and the security forces left seven dead and more than 260 wounded, the worst violence in a week.
"I am going to Egypt to reinforce our message that there must be a fully inclusive political process, taking in all groups which support democracy," Ashton said in a statement before her trip. "I will underline that Egypt needs to return as rapidly as possible to its democratic transition."
Mohamed Bishr, a member of the Brotherhood's 17-strong advisory council and former minister in Mursi's government, told Reuters he and others would meet Ashton "to express our position on legitimacy and democracy with the hope that they will aid democracy and respect the choices made by the Egyptian people".
The ousted president has been held at an undisclosed location and has not been charged with a crime, although the authorities have announced investigations into complaints of spying, inciting violence and wrecking the economy. Prosecutors have also reopened a 2011 jailbreaking case dating to Mursi's escape from brief detention during protests against Mubarak.
The interim cabinet is charged with implementing a faster-than-expected army-backed "road map" to restore civilian rule, which foresees parliamentary elections in as few as six months.
Its main task is salvaging an economy wrecked by two and a half years of turmoil. For that, it has been given a lifeline of $12 billion in aid from rich Gulf Arab states.
Many of the new cabinet ministers are supporters of deep economic reforms demanded by the International Monetary Fund in return for a stalled rescue loan, but investors are sceptical those reforms will be implemented soon. The new planning minister has said it is too soon to restart IMF talks and the Arab cash is enough to sustain Egypt through its transition.
Ashton could offer the EU as a potential mediator. Brussels is not as big a donor to Egypt as the United States but is also less polarising, and tried in the past to mediate between Mursi and his opponents as an honest broker.
On her last visit, in April, Ashton attempted to persuade Mursi to sign up to a power-sharing deal brokered by an EU envoy with Mursi's opponents. Mursi did not respond.
Mursi's supporters say he has been "kidnapped". A military spokesman said he was being held for his own protection.
Mursi was "not detained, but the armed forces took certain measures for his protection, because he has supporters and opponents and in light of the lack of stability in the Egyptian streets," the spokesman, Ahmed Mohamed Ali, told Al Arabiya TV.
He denied that the military was involved in politics: "There is no presence for us on the political scene. There is a president for the state, and a cabinet has been formed. We are out of the picture totally and do not desire rule."
The new cabinet includes the armed forces chief that ousted Mursi, Abdel Fattah al-Sisi, in the joint roles of first deputy prime minister and defence minister.
The Brotherhood has maintained a vigil into its third week, with thousands of supporters camped out in a Cairo square vowing not to leave unless Mursi is restored. It has called protests attracting tens of thousands of people every few days.
Running street battles in the early hours of Tuesday were the deadliest in a week. Before that, more than 90 people were killed in the first five days after Mursi was removed, more than half of them shot dead by troops outside a Cairo barracks.
Military spokesman Ali accused the Brotherhood of mounting "a campaign of incitement that attempts to depict political differences as religious differences. There is incitement to target military installations and headquarters, and this is something totally unacceptable in Egypt or in any country."
The authorities have charged the Brotherhood's main leaders with inciting violence during the protests, although in most cases they have not followed through with arrests.
In the lawless Sinai peninsular bordering Israel and the Palestinian Gaza Strip, Islamist militants have called for an uprising against Egypt's military after Mursi's ouster.
At least 13 mainly security personnel have been killed there since July 3, and late on Tuesday assailants used rockets and machine guns to attack an Egyptian army camp near Rafah, a town straddling Sinai and Gaza. Two soldiers were wounded.