Thousands of Egyptians protested against the state on Tuesday in a rare show of strength to mark what online activists said was a Day of Wrath inspired by the revolt that toppled Tunisia's president.

Web activists have become some of the most vigorous critics of Egyptian President Hosni Mubarak's three decades in office. They led the calls for protests against poverty and repression on what is a national holiday in Egypt.

The protests are being watched to see whether online calls for change can lure Egyptians into the street. Total numbers were difficult to estimate because of the spread of protests, but witness accounts suggested it reached several thousand.

Down, down, Hosni Mubarak, protesters chanted outside a court complex before marching along a road in central Cairo.

Witnesses said about 1,000 joined that march and hundreds gathered in other areas of Cairo, an unusually large number in the Arab world's most populous nation, where protests tend to be swiftly crushed and rarely gather more than a few hundred.

It was also rare that police let protesters march away from a single spot, although there was pushing and shoving between police and protesters trying to get to Tahrir, a big square in the centre of the sprawling capital of 20 million.

Hundreds more gathered in cities outside Cairo, including in north Sinai, Ismailia, Suez and Alexandria, witnesses said. About 200 protested in Mahalla el Kubra, where there were riots in 2008 over subsidised bread shortages and high prices.

Where are you freedom? protesters in Ismailia shouted.

Gamal, tell your father Egyptians hate you, protesters in Cairo shouted referring to Mubarak's son who many Egyptians believe is being groomed to succeed his 82-year-old father. Father and son deny any such plan.

In north Sinai, witnesses and a security source said dozens of protesters lit tyres and blocked a coastal road to Rafah on the border with Gaza, calling for prisoners to be released. The area has seen tensions between Bedouin and police.

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The Interior Ministry warned earlier that it would deal firmly with anyone breaking the law and said demonstrators could face arrest, although it welcomed stationary protests for a limited period.

We have orders not to clash with them (protestors), one security officer was heard to say, speaking on a mobile phone.

Plain clothes police are often used to disrupt Egyptian demonstrators. In one location in Cairo, a witness saw police taking off their uniforms and dressing in civilian outfits.

Tunisian protests that toppled President Zine al-Abidine Ben Ali sent shockwaves through the Arab world. Many Arabs face the same issues that provoked Tunisians to rise up: soaring food prices, unemployment and authoritarian rule.

Ben Ali fled to Saudi Arabia, and some of the Cairo protesters chanted: Oh Mubarak, Saudi Arabia awaits you.

We are protesting against all the laws that have led to the worst living conditions, covering health to education. All we want is to work that's all, said Tobar, an owner of a sportswear shop which he said had to close down.

Egypt's registered opposition parties are weak and fragmented. The banned Muslim Brotherhood, seen as having Egypt's biggest grassroots network, has not called on members to take part but said some would join in a personal capacity.

I will go to the streets on the 25th of January because this country is my country and I vow an oath that I am ready and willing to die for its sake, wrote Mohamed M on a Facebook group that called for protests and which has 87,000 supporters.

Facebook users shared photos before the protests of areas where police had gathered in force or blocked streets. One Twitter entry urged police to join the people's side.

In my book, if you get a tenth of the 80,000 people or so who support the initiative online, it will be a success, wrote Issandr El Amrani on his blog arabist.net before the protests.