About 10,000 to 15,000 mostly US but also Iraqi troops are taking part in the offensive.
US forces struck a railway station in Falluja with small arms and tank machine gun fire, as fighting raged in the besieged Iraqi city.
Warplanes staged ferocious strikes on targets after US-appointed interim Iraqi Prime Minister Iyad Allawi gave US-led forces the go-ahead for a full-scale attack on Monday afternoon.
Aircraft struck about eight times in 20 minutes, sending huge plumes of smoke billowing up from the northwest of the city.
After intense air strikes, artillery barrages and tank fire, US marines launched the full assault two hours after sundown, when Iraq's Muslims mark the breaking of their daily fast during the month of Ramadan.
On one edge of the city, between thunderous explosions, a cleric at a mosque rallied fighters for the battle.
"God is greatest, oh martyrs. Rise up mujahidin," he said, telling fighters that waging jihad was an honour.
Doctors said at least 15 civilians had been killed. There
was no word on early US casualties. Medical sources also told Aljazeera that dozens were injured during clashes between fighters and US-led forces.
Iraqi forces seized the main
hospital in Falluja on Sunday
Iraqi journalist Abu Bakr al-Dulaimi told Aljazeera the clashes were the most violent the city had witnessed since April 2003.
"US tanks, armoured vehicles, F-16 and C-130 fighters are taking part in the attack on Falluja," he said.
"Violent clashes are now going on in the western areas of the city. US forces are backed by tanks and helicopters", he added.
"Clashes have also erupted in Julan neighbourhood. Resistance in these areas is fierce," he said. "The city's defenders are responding to the US attacks with everything at their disposal."
US forces hit
The journalist said clashes also spread to the western parts of the city including al-Jisrain area. US F-16 fighters also bombed sites in northeast Falluja.
Fighters caused some damage to the advancing US forces, hitting two tanks in the northwestern area of Saqlawiya and seven oil tankers in Qarma in the northeast.
"An unmanned aircraft was downed in central Falluja and a US military vehicle was burnt behind the new bridge," said al-Dulaimi.
Iyad Allawi gave the go ahead
for the assault
The Shura Council of the Falluja Mujahidin called for international intervention to halt the assault.
It also called on fighters in other Iraqi cities to go to Falluja's aid.
Earlier on Monday, US marines seized control of land around the hospital on the western edge of the city, witnesses said.
Allawi said he had given US and Iraqi forces the green light to clear the city of what he called terrorists.
"We are determined to clean Falluja from the terrorists," he said in the capital Baghdad.
The US army closed all roads leading to the besieged city after Iraq's interim government declared a 60-day state of emergency throughout the country excluding Kurdish areas, sources told Aljazeera.
The US military says 1000 to 6000 fighters - Saddam Hussein supporters and foreign fighters led by al-Qaida ally Abu Musab al-Zarqawi - are holed up in Falluja's alleyways and on rooftops.
Peace talks between the interim government and Falluja have fallen through several times, most recently last month when Allawi threatened another attack if residents did not surrender al-Zarqawi and other suspected al-Qaida linked fighters.
But residents of Falluja say neither al-Zarqawi nor members of al-Qaida are present.
Al-Zarqawi's group has claimed some of the bloodiest attacks in Iraq in recent months as well as the beheadings of foreign captives.