The US military has promised to take steps to restore law and order in Iraqi cities, where the fall of Saddam Hussein's regime has led to widespread looting and violence.
US marines are still focusing on the military threat
Brigadier-General Vincent Brooks told correspondents at US central command headquarters in Qatar that the situation was "unacceptable".
A US marine was shot dead by two men on Saturday while manning a checkpoint near a hospital.
Fellow marines opened fire and killed one man who was found to be carrying Syrian papers. The other escaped.
The military focus now appears to be switching to the north with US-led reinforcements heading from Baghdad to the Kurdish areas or Tikrit, Saddam Hussein's home town and a possible remaining stronghold.
A CNN crew was able to drive through checkpoints into Tikrit which appeared to still be under the control of the Baath Party.
The team was told to get permission from the area's governor to film and then came under heavy pistol and machine-gun fire as it drove through the city.
Earlier, the journalists were able to film at an abandoned military base. There were no signs of battles but there was evidence of destruction from coalition air strikes.
In other developments:
In Baghdad, US Chinook helicopters carried out their first air patrols in an effort to improve security.
- US Secretary of Sate Colin Powell tells the BBC that once the war is over, the US will concentrate on finding weapons of mass destruction
- The leader of the Iraqi National Congress, Ahmed Chalabi, says 'free Iraqi forces' will go to Baghdad to help with security
- An armed mob reportedly surrounds the Najaf house of a pro-Western Shia cleric, Ayatollah Mirza Ali Sistani, and is giving him 48 hours to leave the country
- China says its embassy in Baghdad has been ransacked, and calls on the US to take urgent measures to restore order
Private Jessica Lynch, who was rescued from Iraqi captivity, has arrived back in the US and been taken to hospital for treatment along with other wounded soldiers
US marines have taken the town of Kut in eastern Iraq, potentially opening up a new supply corridor to Baghdad from the south
Coalition commanders say troops have already secured a hospital in the capital and a water treatment centre threatened by looters.
But they insist that it is unrealistic for their forces to restore law and order in areas where they are still encountering armed resistance.
Looting spread to new areas of Baghdad on Saturday.
General Brooks said some of the violence had been a form of retribution against the former regime, but some had clearly gone beyond that.
The Red Cross has described the overall humanitarian picture in Baghdad as extremely difficult with many hospitals shut because of looting.
In some affluent neighbourhoods, residents have formed vigilante gangs to beat off looters targeting their properties.
However, US forces say they are focusing on eliminating pockets of resistance from supporters of Saddam Hussein.
The Americans also say they have discovered about 300 suicide-bomb vests - many of them packed with explosives.
The BBC's Andrew North says a battalion of American marines has moved into the al-Quds district of north-east Baghdad, where they believe fighters still loyal to Saddam Hussein might be hiding.
In his weekly radio address on Saturday, US President George W Bush warned that "hard fighting" might still lie ahead for US forces trying to defeat remaining pockets of resistance.
Meanwhile, a senior aide to former Iraqi President Saddam Hussein, General Amir al-Saadi, surrendered to US forces in Baghdad on Saturday.
Al-Saadi was on America's wanted list
The general - Saddam Hussein's liaison with UN weapons inspectors in Iraq - is the first from a list of 55 high ranking officials wanted by the US dead or alive to give himself up.
General Saadi told German television station ZDF, which filmed his surrender, that he did not know Saddam Hussein's whereabouts.
He also said he had always told the weapons inspectors the truth, and insisted that Iraq did not have weapons of mass destruction.
The BBC's Nick Childs in Washington says the Americans are keen to question the general but his potential significance remains unclear.