Dozens of Sunni mosques are reported to have been targeted and six Sunnis killed after a gang blew up the dome of the al-Askari shrine in Samarra.
Iraq's top Shia cleric, Grand Ayatollah Ali al-Sistani, has appealed for calm and called for a week of mourning.
Iraqi President Jalal Talabani said the country must work to avoid a civil war.
In a television broadcast, Mr Talabani, a Sunni Kurd, accused the attackers of trying to sabotage attempts to form a coalition government.
"We must... work together against... the danger of civil war," he said.
"I hope that both sides acknowledge that whoever executed this act of religious terrorism is seeking only to fan the flames of hatred and spark civil war"
Saleh al-Mutlaq, a leading Sunni politician in Iraq, told the BBC the emergence of a new broad-based government was critical.
"If we do not act in a very positive way to create a government of national unity, a government which contains everybody, a government which can control the security in Iraq, if we stay as we are now, we kill our men... then we're very near [to] civil war," he said.
No-one has claimed responsibility for the attack on the shrine, although Iraqi television said several people had been arrested in connection with the bombing.
The BBC's Jon Brain in Baghdad says the attack was almost certainly designed to raise the existing tensions between the majority Shia and minority Sunni populations.
Clashes
Following the attack, thousands of demonstrators gathered near the shrine, waving Iraqi flags and calling for justice.
"We demand an investigation so that the criminals who did this will be punished," one of the protesters, 28-year-old Mahmoud al-Samarie, told the Associated Press news agency.
"If the government fails to do so, then we will take up arms and chase the people behind this attack."
Protests and violence broke out across Iraq:
National mourning
The al-Askari shrine is one of two shrines in Samarra for revered Shia imams, which attract pilgrims from around the world.
Iraq's search for unity
The golden dome of the shrine - part of the Imam Ali al-Hadi mausoleum - was reduced to a shell of brown masonry and twisted metal.
Despite soaring anger, Ayatollah Sistani, widely regarded as a moderate, urged Shias not to attack Sunni Muslims or their holy places and called a week of national mourning.
Iraq's Prime Minister Ibrahim Jaafari, a Shia, appeared live on television to declare three days of mourning.
Firebrand Shia cleric Moqtada Sadr cut short a visit to Lebanon on hearing news of the attack.
British Prime Minister Tony Blair condemned the attack and urged Iraqis not to retaliate.
"The perpetrators of this act had one motive and one alone. They want to cause strife and violence between Sunni and Shia to derail democracy," he said.
US President George W Bush said: "This senseless crime is an affront to people of faith throughout the world."
Washington's ambassador to Iraq, Zalmay Khalilzad, and the top US commander in the country, Gen George Casey, said the US would contribute to the shrine's reconstruction.
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