The earthquake, measuring 6.3 on the Richter Scale, struck at 0528 this morning. Reports suggest that the city has been completely destroyed and there are reports that many people remain trapped under the rubble.
Initial estimates suggested 5,000-6,000 people died in the earthquake, the official IRNA news agency quoted a senior official as saying.
Mohammad Ali Karimi, governor of Kerman province, where Bam is located, was said to have given the figure in a telephone conversation with President Mohammad Khatami.
Iranian television said about 70 per cent of the buildings in the historic city, a popular tourist destination some 600 miles southeast of the capital, Tehran, had collapsed and many people were feared trapped under the rubble.
Witnesses said many houses had been flattened and squares were packed with crying children and people left without a home, huddled in blankets to protect them from the cold.
Distraught relatives wept next to corpses shrouded in blankets. Hundreds of bodies were bundled into trucks. Mechanised diggers hollowed out trenches where the dead were buried quickly without rites.
"I have lost all my family. My parents, my grandmother and two sisters are under the rubble," said Maryam, 17.
One old woman, disconsolate with grief, smeared her face with dirt, only able to utter: "My child, my child".
Iranian television said around 30,000 people were injured in and around the city, which had a population of some 200,000 people.
Angry people accused the government of doing nothing to help them and said they were still without tents, water and heating.
Witnesses said the road to Bam was choked with ambulances and people desperate to find family members.
State media said two of Bam's hospitals had collapsed, crushing many of the staff, and remaining hospitals were full. The wounded were ferried to neighbouring towns.
Foreign Ministry spokesman Hamid Reza Asefi told journalists Iran urgently sought sniffer dogs, blankets and medicines from the international community.
A large part of Bam's ancient citadel, one of Iran's best-loved tourist magnets, has been destroyed. The citadel, dating back 2,000 years, contained fortifications, towers, buildings, stables and a mosque.
Bam was located on the old Silk Road route between China and Europe used by merchants and travellers for centuries, and contained inns, a gymnasium, a theological school and bazaars, according to tourism Web sites.
The quake struck when most people in the city would have been asleep. The government mounted an immediate rescue operation in the date-growing area where houses are traditionally made of mud-brick.
Quakes are a regular occurrence in Iran, which is crossed by several major faultlines in the earth's structure.
In June last year, a tremor measuring 6.3 on the Richter scale hit northern Iran, killing at least 229 people and injuring more than 1,000.
Some 35,000 people were killed in 1990 when earthquakes of up to 7.7 on the Richter scale hit the northwest of Iran. Tehran was hit by a quake of about seven on the Richter scale in 1830.