* Suicide bomber targets security compound in Cairo
* Two more explosions in and around capital
* Anger on streets against Egypt's Muslim Brotherhood (Adds one killed in clashes)
By Asma Alsharif and Maggie Fick
CAIRO, Jan 24 (Reuters) - A suicide car bomber blew himself up in the parking lot of a top security compound in central Cairo on Friday, killing at least four people in one of the most high-profile attacks on the state in months, security sources said.
The early morning explosion damaged the Cairo Security Directorate, which includes police and state security, and sent smoke rising over the capital. It also raised concerns that an Islamist insurgency was gathering pace.
Tensions were rising in other parts of Cairo, which has seen numerous protests and street violence since the army deposed Islamist president Mohamed Mursi in July after mass protests against his rule.
Fierce clashes broke out between Mursi supporters and security forces on the road leading to the Pyramids of Giza, where about 2,000 Islamists gathered. Some burned tyres and hurled petrol bombs at police, who responded by firing tear gas.
Clashes were also reported on Friday in Suez City, Ismailia Alexandria and Beni Suef, where one person was killed, security sources said.
Hours after the first bomb attack, two smaller blasts were reported in the capital and its environs.
A crude explosive device killed one policeman and wounded nine others in another Cairo neighbourhood, the Interior Ministry said in a statement. Security sources said a person driving past security vehicles had hurled a hand grenade in their direction.
In Giza, a large district on the outskirts of Cairo, a third explosion went off near a police station. There were no immediate reports of casualties.
The dead from the first blast at the parking lot included three policemen, security sources said. State television quoted the Cairo governor as saying 50 people were wounded.
The attack also heavily damaged the nearby Islamic Art Museum, an official told the state news agency.
In a statement, the office of President Adly Mansour said it would "avenge the deaths of the martyrs" who died at the Security Directorate and severely punish the perpetrators.
TURMOIL AND VIOLENCE
Reuters witnesses heard gunfire immediately after the blast, which twisted metal and shattered the windows of nearby shops. Wood and metal debris was scattered hundreds of metres around.
One body covered in a blanket lay in a pool of blood near a scorched car engine.
State television quoted witnesses as saying gunmen on motorcycles opened fire on buildings after the explosion.
There was no immediate claim of responsibility for the parking lot attack, which came a day before the third anniversary of the uprising that toppled autocrat Hosni Mubarak and raised hopes of a stable democracy in the Arab world's biggest nation.
Instead, relentless political turmoil has hit investment and tourism hard in Egypt, which has a peace treaty with neighbouring Israel and controls the Suez Canal.
After ousting Mursi, army chief General Abdel Fattah al-Sisi unveiled a political road map he said would bring elections and calm to Egypt.
Security forces have killed hundreds of Brotherhood members and jailed thousands more, including top leaders.
The army-backed government has effectively removed the Brotherhood from politics and many Egyptians turned against it after Mursi's troubled one-year rule.
Intense pressure on the movement has severely hurt its ability to stage mass protests it had hoped would reverse what it calls an army coup that has undermined Egypt's democratic credentials.
MILITANT ATTACKS ON THE RISE
But authorities are struggling to contain Islamist militant violence. Militants based in the Sinai have stepped up attacks on security forces since Mursi's fall, killing hundreds, and Egypt's political transition has stumbled.
Attacks in other parts of Egypt have also risen, fuelling fears the country could face an Islamist insurgency similar to one that raged in the 1990s before Mubarak stamped it out.
The Sinai-based Islamist militant group Ansar Bayt al-Maqdis said in December it was behind a car bomb attack on a Nile Delta police compound that killed 16 people and wounded about 140.
On Thursday, gunmen killed five policemen at a checkpoint south of Cairo, the Interior Ministry said.
Prime Minister Hazem el-Beblawi condemned the Cairo Security Directorate attack in a statement, saying it was an attempt by "terrorist forces" to derail the political road map which was nevertheless being implemented "firmly".
The police headquarters assault will likely encourage the state to crack down harder on the Brotherhood, which it accuses of terrorist acts. The group says it is a peaceful movement.
Human rights groups accuse security forces of widespread human rights abuses in their crackdown on the Brotherhood. But the group has little sympathy on the street.
The mood was tense at the site of Friday's suicide bombing. "Traitors and dogs!" yelled onlookers, an apparent reference to the assailants.
People also chanted anti-Brotherhood slogans. "The people want the execution of the Brotherhood. Execution for Mursi," they yelled.
One woman, Wafaa Ahmed, was crying outside the Cairo Security Directorate.
"These people have no sense of loyalty to the nation. This is terrorism, they want to get back at us because we finished them off ...," she said. "Something like this will only make the people stronger and more determined." (Additional reporting by Shadia Nasralla; Writing by Michael Georgy; Editing by Gareth Jones and Hugh Lawson)