* Major pro-, anti-Mursi protests called for Friday
* Brotherhood proposes first crisis talks via EU envoy
* EU says both sides far apart (Adds president to give speech)
By Noah Browning and Crispian Balmer
CAIRO, July 18 (Reuters) - Egypt's Muslim Brotherhood called for mass protests on Friday in its campaign to reverse the army's overthrow of the elected Islamist president, but it also gave a first sign of willingness to negotiate with its opponents.
The rallies aim to show Mohamed Mursi's supporters are not ready to accept the new military-backed government. However, a Brotherhood official also told Reuters on Thursday that the movement had proposed a framework for talks mediated by the EU.
Sworn into office on Tuesday, the cabinet of interim premier Hazem el-Beblawy busied itself with tackling the nation's many woes, buying foreign wheat to replenish stocks and banking $3 billion in badly needed aid from the United Arab Emirates.
Egypt's interim President Adli Mansour will address the nation on Thursday at 9 p.m. (1900 GMT), state TV said. The speech comes on the eve of planned mass pro- and anti-Mursi rallies. It will be Mansour's first speech since he was sworn in on July 4.
Still stunned by the July 3 toppling of Mursi, his Muslim Brotherhood, and allies grouped in what it calls the National Alliance for Legitimacy, urged nationwide rallies on Friday, predicting millions would take to the streets.
"To every free Egyptian man and woman: Come out against the bloody military coup," the alliance said in a statement.
Brotherhood official Gehad el-Haddad, who represented the movement in previous EU-facilitated talks with other political groups, told Reuters that the organisation would not retreat from its demand for the reinstatement of Mursi, Egypt's first freely elected leader.
However, signalling for the first time a formal readiness for negotiations, he said the Brotherhood had proposed through an EU envoy a framework for talks to resolve Egypt's crisis. "We never close the door to dialogue," Haddad said.
The EU envoy, Bernardino Leon, said the two sides remained far apart. It is hard to imagine the army letting Mursi return to power. The military has denied orchestrating a coup, saying it intervened to prevent chaos following mammoth protests on June 30 against Mursi's much-criticised, year-long rule.
Egypt, the most populous nation in the Arab world, is a strategic hinge between the Middle East and North Africa and has long been a vital U.S. ally in the region.
The African Union warned on Thursday that Egypt risked being engulfed by civil war unless its government embraced Islamists - none of whom were included in the 33-strong cabinet.
Egypt's Nour Party, the country's second-biggest Islamist group which had initially backed a military-led roadmap to guide the country to new elections, said on Thursday the government would have to seek a way forward with the Muslim Brotherhood.
"I believe that those in power need to realise that increasing pressure on the Muslim Brotherhood and playing down the emotions of their supporters will lead to extremely bad results," Nour party spokesman Nader Bakkar told Reuters TV.
At least 99 people have died in street clashes since Mursi's downfall, more than half of them when troops fired on Islamist protesters outside a Cairo barracks on July 8.
A security source told the official Middle East News Agency that policing would be intensified at "all important and vital facilities" on Friday.
Tamarud, the movement which organised the massive anti-Mursi protests, has also called for rallies on Friday, including one close to a Cairo intersection where thousands of Brotherhood supporters have been holding a vigil for weeks.
It dubbed the rallies "the people against terrorism", blaming Mursi followers for recent violence.
Three members of the security forces died overnight in attacks blamed on Islamist militants in the Sinai peninsula, which borders Israel and the Gaza Strip. The militants have pledged to continue the fight until the return of Mursi, who has been held in an undisclosed location since his downfall.
Among the many accusations leveled against Mursi was mismanagement of the economy. The budget deficit has soared to about $3.2 billion a month, foreign reserves are more than 50 percent below their December 2010 levels and unemployment is more than 13 percent.
Bread has traditionally been one of Egypt's most explosive issues and an ex-minister from Mursi's government said last week that the country had less than two months' supply of imported wheat in its stocks, well below its preferred six-month supply.
Looking to narrow the shortfall, Egypt's main wheat-buying agency, the General Authority for Supply Commodities (GASC), bought 300,000 tonnes of wheat from global suppliers - only the second such purchase since February.
The cash-strapped government got a fillip with the arrival of the UAE aid, part of $12 billion that Gulf Arab states pledged after Mursi's removal. Saudi Arabia is due to transfer $2 billion in the coming days, Egypt's central bank said.
The funds should buy the cabinet time to try and fix Egypt's numerous problems, although analysts have warned it might also persuade officials to delay difficult decisions needed to right the listing economy. (Additional reporting by Edmund Blair, Peter Graff, Alexander Dziadosz, Yasmine Saleh and Shadia Nasralla; Editing by Alastair Macdonald and Michael Roddy)