* Six soldiers killed, grenades fired at satellites
* Army chief says he told Mursi in February he had failed
* Turmoil hammers tourism
* More protests expected this week
By Shadia Nasralla and Yara Bayoumy
CAIRO, Oct 7 (Reuters) - Suspected militants killed six Egyptian soldiers near the Suez Canal and fired rocket-propelled grenades at a state satellite station in Cairo on Monday, suggesting an Islamist insurgency was gathering pace three months after an army takeover.
Dozens of supporters of the Muslim Brotherhood were killed in clashes with security forces and political opponents on Sunday, one of the bloodiest days since the military deposed Islamist President Mohamed Mursi in July.
The death toll from that day's violence across the country rose to 53, state media said, with 271 people wounded.
The Brotherhood denies the military's charges that it incites violence and says it has nothing to do with militant activity, but further confrontations may shake Egypt this week, with Mursi's supporters calling for further protests this week.
They are likely to be angered by the publication of an interview with Egypt's army chief on Monday in which he said he told Mursi as long ago as February he had failed as president.
Sunday's clashes took place on the anniversary of the 1973 war with Israel - meant to have been a day of national celebration. The countries signed a peace agreement in 1979.
Authorities had warned that anyone protesting against the army during the anniversary would be regarded as an agent of foreign powers, not an activist - a hardening of language that suggested authorities would take a tougher line.
The Muslim Brotherhood accused the army of staging a coup and working with security forces to eliminate the group through violence and arrests, allegations the military denies.
Sinai-based militants have stepped up attacks on the security forces since the army takeover and assaults like that in Cairo's Maadi suburb fuel fears of an Islamist insurgency like one in the 1990s crushed by then President Hosni Mubarak.
Two people were wounded in the attack on the state-owned satellite station while medical sources said three were killed and 48 injured in a blast near a state security building in South Sinai. A witness said it was caused by a car bomb.
"Unidentified people opened fire on a satellite receiver station in the neighbourhood of Maadi in Cairo," the Ministry of Interior said in a statement. Security sources said assailants fired two rocket-propelled grenades at the site.
Security sources said gunmen opened fire on the soldiers in Ismailia while they were sitting in a car at a checkpoint near the city on the Canal, a vital global trade route.
Traffic flowed freely in the centre of Cairo where Sunday's clashes had taken place and state radio said security forces were in control of the country.
But attacks in Cairo like Monday's on the satellite station could do further damage to Egypt's vital tourism industry.
David Hartwell, a Middle East analyst at IHS Jane's, said more explosive devices seemed to be being used in the capital.
"It suggests that Sinai groups are infiltrating in greater numbers in to northern Egypt," he said. "Either these groups are expanding out of Sinai, he said, "or the capabilities that they have is being used by other groups that may or not be affiliated with the Brotherhood."
Army chief General Abdel Fattah al-Sisi, who has promised a political roadmap that would lead Egypt to free and fair elections, said in the interview published on Monday that Egypt's interests differed from those of the Brotherhood.
"I told Mursi in February you failed and your project is finished," privately-owned newspaper al-Masry al-Youm quoted Sisi as saying.
Militant attacks, including a failed assassination attempt on the interior minister in Cairo in September, are deepening uncertainty in Egypt along with the power struggle between the Brotherhood and the army-backed government.
Neither side seems willing to pursue reconciliation, raising the possibility of protracted tensions in U.S. ally Egypt.
Almost daily attacks by al Qaeda-inspired militants in the Sinai have killed more than 100 members of the security forces since early July, the army spokesman said on Sept. 15.
Security forces smashed pro-Mursi protest camps in Cairo on Aug. 14, killing hundreds of people. In an ensuing crackdown, many Muslim Brotherhood leaders were arrested in an attempt to decapitate Egypt's oldest Islamist movement.
The Brotherhood, which had proven highly resilient after previous crackdowns, has embarked on a strategy of staging smaller protests to avoid action by security forces.
Sisi denied Brotherhood allegations that the army had intended to remove Mursi through a coup, saying it had only responded to the will of the people.
Before Mursi's overthrow, Egyptians disillusioned with his year-long rule had held huge rallies demanding that he quit.
Last month, a court banned the Brotherhood and froze its assets, pushing the group, which had dominated elections held in Egypt after Mubarak's fall in 2011, further into the cold.
For many of its supporters, who helped give Mursi 25 percent in the first round of last year's presidential vote, there is no going back on that electoral success. Yet many other Egyptians are only too glad to turn their backs on the Islamists.
"We will not give up. It's either victory or martyrdom for us," said Rami Hammam, a 33-year-old engineer after a pro-Brotherhood rally in Cairo on Sunday. "We want to send a message to the army that the will of the people is above anything else."
While deadly clashes broke out between security forces and marchers, a few streets away thousands of people were chanting Sisi's name in Tahrir Square during festivities glorying in the army on the 40th anniversary of its last attack on Israel.
"I love my country and I want to salute my army. There's no difference between the army of 1973 and the army of 2013," said Ola Sakr, a 25-year-old computer programmer, adding that the Brotherhood was wrong to try and interrupt the celebrations.
Throughout Sunday, state television broadcast ceremonies marking the anniversary of the Yom Kippur War, which ultimately led to Egypt regaining the Sinai in a U.S.-brokered peace treaty. Dance displays, light shows and songs regaled General Sisi while the main media gave little coverage to the protests.
Many Egyptians, not motivated to demonstrate their love for the armed forces, have nonetheless welcomed relative stability since the military takeover and show little sympathy for the troubles of the Islamist movement which tried to govern them.
As bloodied supporters of Mursi were being rushed to an ill-equipped suburban hospital, people in the neighbourhood were smoking water pipes on sidewalks, willing on Cairo's Al Ahly in an African Champions League soccer semifinal in Cameroon.
Surveying the wreckage left by street fighting, with tear gas still on the air and security forces on guard, Sami Afifi, a 53-year-old driver, said the Brotherhood had to back down:
"The Brotherhood can't keep doing this. We want stability. We want people to work," he said, as army helicopters trailing national flags flew in formation overhead. "When I see the clashes it makes me want to join the army and cheer them on."