Alain Pasche, a member of a UN rescue coordination team, said on Monday operations to find survivors of the devastating earthquake would last for at least one more day.
More than 2000 people have been pulled alive from rubble, said the head of the Iranian Red Crescent rescue operations, Bijan Daftari.
"The search to find more people alive is continuing with the help of domestic and foreign rescue workers using sniffer dogs," he told the state news agency IRNA.
But rescuers said they were no longer finding survivors - only the mangled remains of people killed when the world's most lethal quake in at least a decade levelled much of the ancient Silk Road city.
Round-the-clock relief efforts in Bam, 1000 km southeast of the capital Tehran, were hampered by piles of bodies in the streets, overflowing cemeteries, bitterly cold nights, rain, aftershocks, confusion and some looting.
Local officials say the toll is now 22,000.
"I believe the (death) toll will reach 30,000," said a government official in Kerman province, where the quake, measuring 6.3 on the Richter scale, struck before dawn on Friday, while most people were still sleeping, and destroyed about 70% of Bam's mostly mud-brick buildings.
President Muhammad Khatami and several government ministers arrived on Monday to inspect damage and rescue efforts.
Khatami acknowledged that "the scale of the tragedy is very high".
"Whatever we do, it will still be too little," he said. "Hopefully, as time goes by, more aid will arrive."
Khatami first flew over the city aboard an M-18 helicopter to get an overview of the damage before touring the town.
Iranian man carries his two sons
to the cemetery
His visit followed one earlier in the day by the country's supreme leader Ayat Allah Ali Khamenei, who also arrived to inspect the damage and the ongoing rescue work.
Khamenei toured the 2000-year-old Bam citadel which was flattened by the quake.
"We share your pain, we have lost our own children, we are going to try to rebuild Bam, but this time more solidly," he told survivors.
Disease warning, looting
Interior Minister Abdolvahed Mousavi-Lari warned that the spread of disease was a threat.
"We have instructed various bodies to immediately start cleaning up. If we don't bring hygiene back to the city we will have major problems," he said.
Aid poured in from around the world to help deal with a disaster that Khatami said his country could not cope with on its own.
Some young men armed with pistols and Kalashnikov assault rifles drove into Bam in vans and stole Red Crescent tents. Others on motorbikes chased aid trucks, picking up blankets thrown out by soldiers.
As cemeteries battled to cope, mullahs, in shirt-sleeves rather than their usual robes and wearing face masks, fought against the dust and smell and tore sheeting to shroud corpses.
There was no time to wash the bodies in accordance with Islamic rituals.
Bodies were brought in blankets, sprayed with disinfectant to guard against disease and tipped into trenches, hollowed out by mechanical diggers.
Although some survivors have been accommodated in tents, others spent a third night in the open in temperatures of 7 degrees Celsius, burning cardboard and any other material they could find to fend off the cold.
Bam's small airport was packed with a dozen or so military and civilian cargo planes delivering aid in the early hours, barely able to find space on the tarmac that handled no more than a few planes each week before the quake.
Red Cross workers prepare a
The airport's arrival hall has been converted into a temporary hospital ward.
A US Air Force C-130 Hercules landed in Kerman with a first delivery of North American aid and the US military said it would ship in about 70 tonnes of supplies originally earmarked for reconstruction in Iraq.
US officials said North American airmen and Iranian soldiers worked together to unload the plane, the first US flight into Iran since the Iranian hostage crisis ended in 1981.
Washington broke ties with Iran after the US embassy was stormed in 1979 and 52 Americans were held hostage for 444 days.
Iran's call to the world for help from anywhere, but Israel, contrasted with its rejection of assistance in 1990 when a quake killed 36,000 people.
Bam, a tourist attraction because of an ancient citadel and other centuries-old buildings, has a history going back to the old Silk Road days when it was a stopover for merchants and travellers between China and Europe.
A large part of the citadel was destroyed by the quake.
In other developments, an Iranian army helicopter crashed while on a relief mission and the two people on board are missing, reported IRNA on Monday.