United States Defence Secretary Donald Rumsfeld is making an unannounced visit to Baghdad, three weeks after US troops seized control of the Iraqi capital.
Mr Rumsfeld said in an address to be broadcast to the people of Iraq that American troops would stay only as long as it took to ensure there was a democratic government.
During his visit, he is expected to meet Jay Garner, the retired US general running Iraq.
As he arrived, US troops opened fire on protesters for a second time this week in the town of Falluja, 50 kilometres (35 miles) west of Baghdad.
Reports say at least two people were killed and eight wounded during a march to protest against the deaths of 13 people on Monday night.
In his letter, "Saddam" promises "liberation and victory".
US military spokesmen say troops were fired on first in both incidents, which occurred outside facilities being used by US paratroops in the town.
A London-based Arabic newspaper, Al-Quds Al-Arabi, has published a letter purporting to come from Saddam Hussein. Dated 28 April and received by fax, it calls on Iraqis to unite against occupation.
The paper's editor, Abdel Bari Atwan, said he believed the letter was genuine as the signature resembled Saddam Hussein's.
Mr Rumsfeld is the most senior US official to visit Iraq since the war to topple Saddam Hussein began.
He flew into Iraq from Kuwait as part of a regional tour, saying he was pleased to "witness the liberation of Iraq".
"Let me be clear: Iraq belongs to you. We do not want to run it," he said in the speech, to be broadcast on radio and
TV frequencies by the US military.
Hello, I'm Don Rumsfeld, the American Secretary of Defence.
I am pleased to visit Iraq - your country - to witness your
The last time Mr Rumsfeld was in Baghdad was in 1983, when as a special presidential envoy to the Middle East he held a secret meeting with Saddam Hussein which correspondents say led to closer US-Iraq ties.
Mr Rumsfeld had spent the morning in Iraq's second city of Basra after flying in aboard an MC-130 aircraft used by special forces for attack and reconnaissance missions.
British troops are in command of Basra, but amid a show of tight security Mr Rumsfeld was surrounded by black-clad US special operations troops as he arrived.
Mr Rumsfeld is on a week-long visit to the Gulf to thank the coalition troops who took part in the campaign as well as regional leaders who provided support.
He is also discussing the reduction of US troop presence in the area.
The defence secretary was greeted at Basra airfield by Major General Robin Brimm, commander of the British 1st Armoured Division, which controls the region around the city.
"What is significant is that large numbers of human beings, intelligent, energetic, have been liberated," Mr Rumsfeld said.
"They are out from under the heel of a truly brutal vicious regime."
Mr Rumsfeld was accompanied by Lieutenant General David McKiernan, commander of the coalition ground forces in Iraq.
Ahmed al-Taha, a senior official at Falluja's main hospital, said two people had been killed during Wednesday's protest and eight were wounded.
The dead Iraqis had head wounds caused by bullets or shrapnel, he said.
Why is there an American military presence? We just want a reduction in
Imam Jamal Shaqir Mahmood
About 1,000 local people from the town - a Sunni Muslim former stronghold of Saddam Hussein's Baath party - had marched down the main street to the battalion headquarters of the US 82nd Airborne Division to protest at Monday's deaths outside a primary school.
Stones and shoes were hurled at the HQ, situated in a compound formerly occupied by the Baath party, and troops opened fire at about 1030 local time (0630 GMT), dispersing the crowd.
There was confusion over whether guards inside the compound or troops from a passing US convoy fired the shots.
Falluja was a bastion of the ousted Baath party
US Major Michael Marti said troops had opened fire after a convoy came under gun attack which began as protesters hurled stones at the vehicles.
"Then fire came from the crowd, directed at the convoy," he said.
"It was at that point that they returned fire... It was well-aimed fire."
Witnesses who spoke to the Associated Press news agency said there had been no gunfire from the direction of the protesters.
Jamal Shaqir Mahmood, the imam at the Grand Falluja Mosque, said people wanted American troops to leave the town or at least reduce their numbers.
"There is no [Iraqi] military presence here," he said. "Why is there an American military presence? We just want a reduction in