The Third Brigade of the US Army's third Infantry Division was circling northward from the west while the Marines launched a pre-dawn push from the southeast towards the Tigris river, said Major Rod Legowski.
"We think by today, it (Baghdad) will be totally surrounded," he said, claiming that Egyptians, Jordanians and Syrians were fighting alongside Iraqi forces against US troops moving on the capital.
The consolidation of US positions around Baghdad came amid a fresh wave of coalition air raids on the Iraqi capital, with explosions and artillery fire rocking the city centre and the southern outskirts, as the war entered its 18th day.
The renewed bombardment followed several raids overnight, with at least two massive blasts in central Baghdad just after midnight (2000 GMT Saturday) which was qualified as unusually powerful.
Late on Saturday a missile plunged into the Tigris river near Saddam's main presidential palace, a frequent target since the outbreak of war on March 20.
But life in the capital appeared relatively normal, with public transportation operating and cafes open.
On Saturday, US troops, who claimed control of Baghdad's main airport on Friday, rode tanks deep into the capital, reportedly killing 1,000 Iraqi troops and claiming they could come and go as they pleased.
But a defiant Saddam later urged his people to resist the US-British invasion, insisting that the ancient city could be saved.
"The enemy has concentrated all its forces against Baghdad, which has weakened its power in other parts of Iraq," Saddam said in an address read on Iraqi state television by information minister Mohammad Said al-Sahhaf.
"You must now weaken them further, deepen their wounds and deprive them of what they have taken of your land, even though it is negligible, in order to reduce their chances and accelerate their defeat," he added.
Saddam was shown on Saturday chairing a meeting of his top aides, including his sons Uday and Qusay, while US President George W Bush conferred with his top advisors at his Camp David retreat and by teleconference.
The Iraqi leader, whose whereabouts have been the subject of rampant speculation among US and British leaders since the start of the war, has recently appeared more frequently on television to show he is still in control.
On Friday, state television aired images of Saddam receiving kisses from a cheering crowd in a residential Baghdad neighborhood.
Bush meanwhile conferred by teleconference with vice president Dick Cheney, Defence Secretary Donald Rumsfeld, Secretary of State Colin Powell, National Security Advisor Condoleezza Rice and other top advisors.
Bush was preparing for a summit in Northern Ireland on Monday and Tuesday with British Prime Minister Tony Blair, his staunchest ally in the campaign to depose Saddam and strip Iraq of its alleged weapons of mass destruction.
"Village by village, city by city, liberation is coming," the US president said in his weekly radio address on Saturday.
At US Central Command's base in Qatar, Major General Vincent Renuart told reporters that Saturday's incursion was "a clear statement of the ability of coalition forces to move into Baghdad at times and places of their choosing."
Iraqi forces put up stiff resistance, with violent clashes taking place in residential and commercial districts. An AFP reporter saw dozens of Iraqi military vehicles burning in the streets after the incursion.
US fighter jets are now flying 24-hour patrols over Baghdad to provide air support for troops on the ground, ahead of the decisive push on the capital to try to break Saddam's 24-year grip on power.
But Sahhaf insisted the coalition had lost more than 300 soldiers in fierce fighting around the airport, a claim denied by coalition commanders.
Meanwhile, the US 101st Airborne Division launched an air assault to secure the Shiite Muslim holy city of Karbala, some 90 kilometers southwest of Baghdad.
In northern Iraq, Qatar-based satellite television channel Al-Jazeera reported on Sunday that US air raids were targeting the regional capital of Mosul.
Kurdish military sources said government troops backed by armor had launched a counter-attack late on Saturday against rebel and US forces at a strategic bridge on the approaches to Mosul.
"The bridge of Khazer is controlled by the two sides," a Kurdish military official said. The report could not be independently confirmed and reporters operating from the Kurdish side were not allowed into the area.
In the south unnamed military sources quoted by Britain's Press Association said British tanks had entered the center of Basra, Iraq's second city.
On Saturday, the US-led coalition said it had bombed the residence of Saddam's cousin and top aide, Ali Hassan al-Majid, in the key port city.
Al-Majid is known as "Chemical Ali" for the ruthless campaign he waged against the Kurds at the end of the 1980-88 Iran-Iraq war.
Al-Jazeera reported 17 Iraqi civilians, including nine children, were killed in Saturday's air strikes on Basra.
Since the start of the war, 80 US soldiers have been killed, eight are listed as missing and seven have been taken prisoner, the Pentagon said on Sunday. The British military has reported 27 troops killed.
In Sydney, Prime Minister John Howard hailed the progress of the coalition campaign, to which Australia has contributed aircraft and special forces troops, but added that it was still too early to declare victory.
"It's gone very well, and the Iraqis do not appear to be putting up any systematic, orthodox military resistance," he said. "That doesn't mean though that it's going to be over shortly."
Elsewhere, Taiwan on Sunday donated $4.32 million in aid to Iraq, including 5,000 tonnes of rice, canned food, medical equipment, tents and blankets.