Speaking to Aljazeera by telephone on Saturday, the spokesman said the US military was suffering increasing numbers of casualties.
"The announcement of the end of the military offensive is proof that American forces are in an impasse ... the American criminals and the Iraqi apostates have suffered more than 150 killed and more than 270 wounded," said Abu Saad al-Dlimi, spokesman of the Shura (consultative) Council of the Muhajidin in Falluja.
Earlier, US-backed Iraqi government officials pronounced the conclusion of a massive six-day US offensive on Falluja.
"Today alone, young freedom fighters have been able to torch more than 12 [American military] vehicles," said the resistance spokesman, adding that the situation had not changed for the past three days.
"US forces are still outside the [northwestern] Julan neighbourhood. US forces were not able to gain one metre of this district," Dlimi added.
"US forces are meeting with fierce resistance from inside Falluja districts ... and are surrounded. They are under missile and artillery fire," he said.
Only pockets left
A senior Iraqi official said earlier on Saturday that the battle to retake the city was over, with more than 1000 fighters killed, but that the country's most wanted man, Abu Musab al-Zarqawi, had fled.
Fighters and journalists say US
troops are facing fierce resistance
"Operation Fajr (Dawn) has been achieved and only the malignant pockets remain that we are dealing with through a clean-up operation," Qasim Dawud, a minister of state, said.
The US military, which spearheaded the six-day assault, said commanders on the ground had yet to declare the operation over.
But a US officer said on Sunday that fighters were showing much less resistance than before.
"Two days ago they were coming out and fighting us. Last night they were running. It looks like we are about to break their will," tank company commander Captain Robert Bodisch said.
Dlimi rejected Dawud's assertions.
"The number of martyrs among young fighters does not exceed 100, the others are unarmed civilians who were crushed by American tanks," said Dlimi.
"If [the Americans] say they have wrapped up operations in Falluja, we are telling them that if that is true allow all satellite networks to enter the city this night so the world can see what is really happening in the streets of Falluja.
"Everything they are announcing is disinformation. Falluja is the theatre of butchery and destruction. Today they bombed the only telecommunications centre which provided links between Falluja and the outside world. Americans are criminals," said the spokesman.
So many pockets
Local journalist in Falluja, Haza al-Afify, told Aljazeera: "Fierce clashes are still under way at the northern and northwestern edges of Julan neighbourhood. Fighting is also raging in the southern and southeastern neighbourhoods, particularly at al-Shuhada neighbourhood and the industrial quarter.
"What we have heard on ending military operations as stated by the Iraqi State Minister for Defence Qasim Dawud does not bear credibility in relation to the reality of the situation on the ground.
"Fierce clashes are still continuing in several neighbourhoods. If these neighbourhoods are mere pockets, Falluja will be harbouring so many pockets."
He added that while US tanks and armoured vehicles had the main roads under control, the narrow alleys were still out of reach to US forces.
"I assure you that the reality of the current situation does not imply a halt to military operations, he said."