Elsewhere in Iraq 17 people died in attacks as US marine intelligence warned that resistance was likely to increase.
The marine and soldier died on Thursday during continuing mop-up operations in the battle-ravaged town. Their deaths raised the toll among US-led forces to 51 US dead and eight Iraqis, the top US marine commander in Falluja said.
US-led troops continued to engage in sporadic battles against the resistance in Falluja after launching a major assault to wrest the town west of Baghdad from armed fighters 10 days ago.
The military shelled the southern outskirts of the town, an AFP photographer said, even after a US marine officer had declared on Wednesday: "The battle is over".
Iraqi volunteers and US troops were able to clear 24 corpses from the battered city and evacuate five civilians, a reporter said.
The Iraqi Red Crescent said 150 families remained stranded.
US troops called in some Falluja
residents to remove corpses
In Iraq's north, a security guard was killed and four wounded in a mortar attack on the governor's compound in Mosul.
A US base in the town was also hit by mortars and six Iraqis died in bombings in the northern oil towns of Baiji and Kirkuk.
A roadside bomb in capital Baghdad killed an Iraqi while fierce clashes erupted between US forces and Iraqi fighters in Ramadi.
US marines may be broadly in control of Falluja but are getting bogged down in risky house-to-house searches.
The response from the US forces has been to use tanks to blast buildings where they suspect fighters may still be holed up rather than face booby traps and sniper fire as they comb through the rubble and narrow alleyways of Falluja.
"Searching every house is taking a long time and it is still dangerous because we never know what is in these homes," Captain Robert Bodisch said.
There are still plenty of fighters around, Bodisch added, although considerable numbers have been surrendering.
Secure, not safe
Meanwhile, the top US marine commander in Iraq said the US-led assault on Falluja had "broken the back of the insurgency" in Iraq by taking away its safe haven, scattering operatives and disrupting its command networks.
"Searching every house
is taking a long time and it is still dangerous because we never know what is in these homes"
Captain Robert Bodisch,
Lieutenant-General John Sattler said on Thursday the town was secure but not safe, with heavy fighting still erupting in some quarters as marines and Iraqi government troops cleared buildings of holdouts.
General Sattler said his forces have not found a location in the town from which Jordanian Abu Musab al-Zarqawi reportedly staged executions and car bombings.
Despite heavy fighting with US-led forces in Falluja, resistance in Iraq is likely to increase in scope and size in the area, a report distributed to senior marine and army officers in Iraq said.
Marine intelligence officials issued a report warning that any significant withdrawal of troops from Falluja would strengthen the resistance, the New York Times said on Thursday.
The pessimistic analysis was prepared by intelligence officers in the First Marine Expeditionary Force (1 MEF) last weekend as the offensive in Falluja was winding down, the daily said.
The US toll in Falluja hit 51 after
another death on Thursday
Although the resistance crumbled in the face of the offensive, the report warned "the enemy will be able to effectively defeat 1 MEF's ability to accomplish its primary objectives of developing an effective Iraqi security force and setting the conditions for successful Iraqi elections".
Senior military officials in Iraq and Washington disputed the findings of the report, describing it as a subjective judgment of some marines that did not reflect the views of all intelligence officials and commanders in Iraq.
"The assessment of the enemy is a worst-case assessment," Brigadier-General John DeFreitas, the senior military intelligence officer in Iraq, said of the report in a telephone interview with the New York Times.