* Tired of post-Mubarak chaos, Egyptians want strong leader
* No competition for Sisi after big crackdown on Islamists
* Muslim Brotherhood accuses him of effective coup (Adds Hagel-Sisi phone call, paragraphs 10-12)
By Yasmine Saleh
CAIRO, Jan 27 (Reuters) - Egypt's top military council gave the army chief, Field Marshal Abdel Fattah al-Sisi, a green light on Monday to seek election as president, a vote he is almost sure to win with Egyptians weary of turmoil unleashed by a pro-democracy uprising in 2011.
Sisi deposed elected Islamist President Mohamed Mursi in July after mass unrest over his increasingly arbitrary and erratic rule, kindling political chaos and security crackdowns on dissent in the Arab world's most populous nation.
He has since taken on almost cult-like popularity in Egypt, with many seeing him as a decisive figure able to stabilise a country that has lurched from one economically ruinous crisis to another since the 2011 overthrow of autocrat Hosni Mubarak.
"(The Supreme Council of the Armed Forces) is looking forward with respect and reverence to the desire of the huge masses of the great Egyptian people in the nomination of ... Abdel Fattah al-Sisi for the presidency of the republic, which it considers a mandate and an obligation," the military high command said in a statement.
"The top army officials all okayed Sisi running for the presidency," said a security source. The 59-year-old career officer is expected to announce his candidacy within days.
Hours before top generals approved Sisi contesting the election, the presidency announced he had been promoted to field marshal from general, in what security officials said was a sign he is about to declare his candidacy for the presidency.
"The decision was expected and it is the first step before the resignation of the general and his candidacy announcement, which is now expected very soon," said a security official.
In order for Sisi to contest the election, he has to resign from his post as defence minister and from the military.
After toppling Mursi, Sisi unveiled a political road map that promised free and fair elections in Egypt, which is of great strategic importance because of its 1979 peace treaty with Israel and control of the Suez Canal.
Sisi and U.S. Defense Secretary Chuck Hagel spoke by phone on Monday, discussing the next steps in the country's political transition and acknowledging the firm U.S.-Egypt partnership in the face of recent militant attacks, a Pentagon spokesman said.
Hagel is considered an important channel of communications with Egypt because of the close military ties between Cairo and Washington.
The United States provides Egypt with about $1.55 billion in aid annually, most of it military assistance. But U.S. officials said in October the United States would withhold some of that assistance, including weaponry and cash, pending progress on democracy and human rights issues.
ISLAMISTS ACCUSE SISI OF COUP
Despite his popularity, Sisi has no pedigree as a democrat and has shown himself willing to apply deadly force against those who disagree with him.
The Muslim Brotherhood accuses him of staging a coup by effectively putting the Egyptian government back under the domination of the military as it was before Mubarak's exit and aborting its professed transition to democracy.
The Brotherhood holds Sisi responsible for what it says are widespread human rights abuses in a security crackdown that has killed nearly 1,000 Islamists. Top Brotherhood leaders including Mursi are all in jail and facing trial.
But in addition to many people in the street, Sisi enjoys the backing of the army, Egypt's most powerful institution, as well as the Interior Ministry, many liberal politicians and Mubarak-era officials and businessmen who have made a comeback since the political demise of Mursi.
Judging by his appeal, those forces are likely to give him plenty of time to prove himself as president, and there are no other politicians who could challenge Sisi anytime soon.
Deputy Prime Minister Ziad Bahaa El-Din, a moderate in the army-backed government, tendered his resignation on Monday.
Bahaa El-Din, a lawyer, had called for a more inclusive political process in a nation that, crippled by prolonged violent unrest that has shattered the economy, appears to be growing less tolerant of dissent by the day.
"A crucial stage of the road map is now over. It required keeping a unified front and avoiding disputes in order for the nation to emerge from constitutional and economic collapse," said a letter posted on Bahaa El-Din's Facebook page said. "Now that we start a new phase where the country is preparing for successive elections ... I ask that you accept my resignation."
Bahaa El-Din is in charge of an economic team that includes the ministers of finance, trade and industry, supply, planning and investment, as well as the governor of the central bank. (Additional reporting by David Alexander in Washington; Writing by Michael Georgy; Editing by Mark Heinrich and Peter Cooney)