* New constitution would open way for fresh elections
* Muslim Brotherhood refuses to back down, stages rallies
* Saudi funds arrive to help bolster state coffers (Adds in paragraph 8 denial of report Mursi formally arrested)
By Maggie Fick and Noah Browning
CAIRO, July 21 (Reuters) - A panel of legal experts started work on Sunday to revise Egypt's Islamist-tinged constitution, a vital first step on the road to fresh elections ordered by the army following its removal of Mohamed Mursi as president.
Mursi's Muslim Brotherhood, which has accused the army of orchestrating a military coup and denounced plans to revise the constitution, staged fresh rallies on Sunday to maintain pressure on the new, interim government.
Setting a highly ambitious timeframe, the military wants new elections in around six months and has tasked a panel of 10 legal experts to present proposed changes to the constitution within 30 days for review before a broader-based body.
The original constitution was approved by a referendum last year, but critics said the text failed to protect human rights, minorities and social justice.
Ali Awad Saleh, a judge and the constitutional affairs adviser for the newly installed president, chaired Sunday's panel, saying it would spend the next week receiving ideas from "citizens, political parties, and all sides".
Khaled Dawoud, a spokesman for the National Salvation Front, Egypt's main secular political alliance, called the start of the committee's work "a very positive development".
The Muslim Brotherhood has shown no sign it is ready to engage with the new administration or the army, sticking firmly to its demand for the full restoration of Mursi, who has been held in an undisclosed location since his downfall on July 3.
Army and judiciary sources denied a report in state-run Al-Ahram newspaper's early Monday edition that the public prosecutor had ordered the arrest of Mursi for 15 days pending an investigation into charges of spying and inciting violence.
A few thousand women, children and men marched from the site of a round-the-clock, pro-Mursi vigil in a Cairo suburb on Sunday, moving to within sight of the defence ministry, ringed by barbed wire and protected by well-armed soldiers.
"Why, Sisi why, why did you kill our sisters?" the crowd chanted, referring to General Abdel Fattah al-Sisi, the defence minister who played a central role in forcing Mursi from office following mammoth street protests against the Islamist ruler.
More than 100 people have died in violent clashes this month, including three women taking part in a pro-Mursi rally in the Nile Delta town of Mansoura on Friday.
Trying to burnish their democratic credentials, the Egyptian military has said the new constitution should be put to a referendum before planned parliamentary elections.
However, some analysts have expressed doubts about rushing to revise the text given the lack of political consensus that has clouded Egypt's faltering transition to democracy in the wake of the 2011 removal of veteran autocrat Hosni Mubarak.
"The problem is not amending or drafting the constitution, the problem is deciding the direction the country is headed," said Zaid Al-Ali of International IDEA, a Stockholm-based intergovernmental organisation.
"Unless political agreement is reached between all of the major political actors in the country, we are going to head from one crisis to another," he said.
Despite the continued domestic tensions, the new government is trying to show the world that business is returning to normal in Cairo. On Sunday, the cabinet held its first meeting since being sworn into office last week.
"The people need to be informed candidly about the size of Egypt's problems, which require quick and decisive action," said a statement issued at the end of the gathering.
Egypt's finances are floundering: the budget deficit has widened to almost half of all state spending and foreign reserves totalled just $14.9 billion in June - representing less than three months of imports that the International Monetary Fund considers to be a minimum safe cushion.
Some of Egypt's Arab allies welcome Mursi's demise and have rushed to prop up the nation's coffers, however.
Egypt's central bank said on Sunday it had received $2 billion in funds from Saudi Arabia, the latest instalment of a $12 billion aid package pledged by Gulf Arab states.
The Egyptian stock exchange rose to a seven-week high on Sunday, encouraged by a lack of violence at weekend "anti-coup" protests in Cairo, hoping it indicated tensions are calming.
However, violence continued in the lawless Sinai peninsula, where three members of Egypt's security forces were killed on Sunday by armed men - the latest in a string of attacks blamed on Islamist militants opposed to the army.
Mursi was Egypt's first freely elected leader, but during his one year in office he drew criticism for failing to revive the ailing economy, restore security or build institutions. The Muslim Brotherhood say they were repeatedly thwarted by remnants of Mubarak's old government and forces hostile to them. (Additional reporting by Shadia Nasralla and Yasmine Saleh in Cairo and Yusri Mohamed in Ismailia; Writing by Maggie Fick and Crispian Balmer; Editing by Sonya Hepinstall)