* Anti-American sentiment deepens
* Egypt could look to Russia for arms
* Saudi and Israeli frustration
CAIRO, Oct 11 (Reuters) - A U.S. decision to curtail military and economic aid to Egypt to promote democracy may ultimately backfire, pushing Cairo to seek assistance elsewhere and giving Washington less leverage to stabilise a country in the heart of the Middle East.
Washington faces a dilemma in dealing with its major regional ally: Egypt controls the Suez Canal and has a peace treaty with neighbouring Israel but its army overthrew the first freely elected president, Islamist Mohamed Mursi, in July.
The United States said on Wednesday it would withhold deliveries of tanks, fighter aircraft, helicopters and missiles to Cairo as well as $260 million in cash aid to push the army-backed government to steer the nation towards democracy.
Egypt's government, the second largest recipient of U.S. aid after Israel, said it would not bow to American pressure. The country's military, which has been leading the crackdown against Mursi's Muslim Brotherhood, can afford to be even more defiant.
Hundreds of Brotherhood members were killed and about 2,000 Islamist activists and Brotherhood leaders, including Mursi, were arrested.
Army chief Abdel Fatah al-Sisi has emerged as the most popular public figure in Egypt, and he is well aware that many Egyptians have both turned sharply against the Brotherhood and bitterly concluded that Washington supports the movement.
At the same time, many Brotherhood members believe the Obama administration was behind what it calls a military coup.
With its credibility in question, Washington has little chance of getting the two sides to compromise and take part in a democratic, inclusive political process.
Even the European Union, which is seen as far more neutral, has made little headway.
LOOKING TO RUSSIA
Most worrying for the United States is the possibility that the Egyptian army -- the largest in the Arab world -- will turn to a rival country for aid after decades of close ties to Washington.
The United States has long provided Egypt with about $1.55 billion in annual aid, including $1.3 billion for the military.
Military officials told Reuters that the country's generals have grown mistrustful of the United States throughout the political crisis that erupted after Mursi's overthrow.
They were infuriated from early on when the United States began hinting that action could be taken to demonstrate Washington's displeasure at Mursi's removal. Military officials said they were not surprised by the reduction in aid.
"There is a saying among us that 'whoever is covered by the Americans is in fact naked'," one military source said.
"Americans shift their positions based on their interests and don't have principles. But we also know that whatever they say or hint they would do, in the end they will not want to lose Egypt."
Egypt's army is exploring its options. "The military definitely has plans to diversify its source of weapons which include going to Russia," said the military source, who did not elaborate.
El Watan newspaper, which is close to the army, quoted a military source as saying that Egypt will soon announce deals for arms from "new markets other than America" which are of the same standard as ones from the United States.
American efforts to sell democracy in Egypt and return the Brotherhood to politics have deepened long-standing mistrust of the United States.
Conspiracy theories about American plans to divide Egypt and the greater Middle East have mushroomed, with some of the plots detailed in diagrams in newspapers.
"Screw the American aid," read one banner newspaper headline in red. In one part of Cairo, a poster of the American president with a white beard reads "Obama is a terrorist".
Military officials buy in to some of the conspiracy theories, including one which suggests that U.S. ally Israel wants Islamists in power in the Middle East to keep the region unstable.
"Islamists ruling Arabs would be enough to ensure that Israel remain the biggest power in the region," one colonel said.
Support from Gulf Arab states such as Saudi Arabia, which were happy to see Mursi go because of their loathing of the Brotherhood, could give Egypt room for manoeuvre if it decides to move away from the United States.
After Mursi was deposed, Saudi Arabia, Kuwait and the United Arab Emirates promised Egypt a total of $12 billion in loans, grants and fuel shipments. The aid has kept the economy afloat and may give Egypt some policy flexibility.
"Compared to Gulf aid, American aid is peanuts. It won't financially affect Egypt and could easily be filled by Gulf countries," said Abdullah al-Askar, chairman of the foreign affairs committee in Saudi Arabia's Shoura Council, an appointed parliament that has only advisory powers.
"People in the Gulf do not see (cutting the aid) as a democratic message. Otherwise why is America allowing the Syrian regime to continue killing people every day?"
Both Saudi Arabia and Egypt -- Washington's most important allies in the Arab world -- are frustrated with U.S. policy and see Washington as an indecisive superpower.
"The U.S. position is not clear and not understood and comes at a time when Egypt needs help," a government official said. "For sure the U.S. will lose the support of the Egyptian people and it is natural that the void it leaves by its loss of the Egyptian people will benefit another power in the world."
Israel also has issues with the American approach in Egypt. Israel welcomed in private the downfall of Mursi and had urged Washington behind the scenes to provide full support to the new military-backed government in Cairo.
"I would not be surprised, by the way, if tomorrow or the day after, the Saudis and others begin to hold talks with the Russians under the carpet in order to ensure there will be a protective umbrella when the time comes," Former Israeli Defence Minister Binyamin Ben-Eliezer told Israel Radio.
Sisi has promised a political road map will bring free and fair elections. He is not under any real pressure from Egyptians to speed up the process, and Egyptian officials won't take it too kindly if the United States keeps pressing the military.
"Any inch Obama loses, another power will gain and we will not mind," said the government official.