By Hamid Ould Ahmed and Lamine Chikhi

ALGIERS, April 11 (Reuters) - Algiers, a city struggling to shed an unhappy past, felt new apprehension about its future on Wednesday after twin bombings that killed 30 people.

As downcast men and women swept up shattered glass from broken windows, many voiced horror at the idea that the violence that haunted Algeria in the 1990s could make a comeback.

"This is a disaster," said lawyer Tahar bin Taleb, 41, who was buying clothes for his baby daughter when the first bomb went off at the prime minister's headquarters.

"This is international terrorism. It signals great danger ahead for southern Europe and north Africa."

One of the blasts, believed to be a suicide bombing, ripped part of the facade off the prime minister's headquarters in the centre of Algiers. A second bomb hit Bab Ezzouar on its eastern outskirts, the official APS news agency said.

Crowds of men and women ran screaming and shouting from the scene after the downtown blast, some saying they feared attackers were planning a second bomb there.

Rumours of fresh bombings filled the air for the next few hours, raising tension around a Mediterranean city that has been an arena of political conflict since French colonial times.

"Algeria has never seen such a powerful explosion. I cannot understand the message," said a government employee, a bandage covering a head wound, near the prime minister's building.

One man recalled a breezy greeting spoken by a policeman guarding the building in the cool of the spring morning as employees arrived for work. They may have been his last words.

"I was in my car in front of the palace smoking a cigarette when the explosion shook my vehicle. I thought it was an earthquake," said the man, who works at the building.

"I will keep in my memory the image of a policeman who said 'Good Morning' to me at the palace gate a few minutes before the explosion. He was killed. God's blessings on him."

The suicide bomber blew himself up when policemen prevented him from forcing a car through a fence at the entrance to the government palace, a policeman said.

On the eastern outskirts, near the new international airport, a second bomb left residents shocked and fearful.

Soraya, a 26-year-old pharmacist who lives near the police station, said: "I was about to leave home when I heard a big explosion. My ears are still hurting.

"Then I saw the smoke above the roof of the police station. The smell of the powder is still present. I saw people running away -- a big panic."

The attacks raised fears the full-scale conflict of the 1990s between the army and Islamist rebels could reignite.

The Al Qaeda Organisation in the Islamic Maghreb claimed responsibility for the bombings in an Internet statement, which also included a claim of responsibility for attacks in neighbouring Morocco and pictures of three "martyrs".

The claim could not immediately be verified.

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