Tony Blair has promised the Iraqi people that US-led coalition forces "will not let you down" as UK troops began firing in support of what they believe is an uprising in Basra.
Tony Blair to meet George Bush
At his monthly news conference ahead of the assault on troop positions in the southern Iraqi city, Mr Blair said the military campaign had already achieved a "huge amount".
He pledged: "Saddam Hussein and his regime will be removed. Iraq will have a better future ahead of it."
Mr Blair said the Iraqi people were wary of rising up against Saddam Hussein's regime after the failure to remove the dictator following the Gulf War in 1991.
Iraq has denied British military intelligence officials' reports of the Basra uprising.
The prime minister was speaking after fierce resistance from paramilitaries in Basra claimed a second British soldier's life.
Coalition forces have continued to advance on Baghdad - although delayed by fierce sandstorms - where they were expecting to meet extremely strong military opposition.
Mr Blair also confirmed that he will fly to meet US President George Bush on Wednesday and Thursday
The prime minister's spokesman said the discussions would centre on post-Saddam Iraq.
Mr Blair is also due to hold talks with UN Secretary General Kofi Annan on Thursday.
Mr Blair said he was sure the war could be won not just because of the abilities of coalition forces but because "the cause is just" and "the vast majority of the Iraqi people want Saddam gone".
In the five days since hostilities began, coalition forces had penetrated twice as far into Iraq as they had done by the end of the 1991 Gulf War, when ground troops moved in after five weeks of aerial bombardment, said Mr Blair.
"We are 60 miles south of Baghdad, a large part of Iraq has been secured and each of the main strategic objectives has been achieved."
Mr Blair said nobody should be surprised that parts of the Iraqi armed forces were determined to fight because they knew when the regime failed they would have nowhere to go.
He said he felt more comfortable now that the aim of the war was also to remove Saddam Hussein's regime from power.
Mr Blair refused to comment on US reports that Saddam Hussein had given the order for chemical weapons to be used in the defence of Baghdad.
But, he said, from the outset the coalition had to be on its "guard about the possibility of Saddam using chemical or biological weapons".
As well as pursuing the military campaign, the coalition was "also determined" to bring humanitarian relief to the people of Iraq, he said.
International Development Secretary Clare Short said on Tuesday the UK was pledging another £30m in aid to be used immediately in Iraq.
The funds will be given to the Red Cross and Red Crescent who are already operating in Iraq, Ms Short told BBC World Service.
Meanwhile, a second British soldier, from the 1st Battalion The Black Watch, has died in combat, near the town of al-Zubayr, about 15 miles (24km) south-west of Basra, on Monday night.
Earlier, the first British soldier killed in combat in Iraq was named by the Ministry of Defence as Sergeant Steven Roberts.
Conservative leader Iain Duncan Smith has said coalition forces should target Iraqi state television and radio, which he said were only broadcasting Iraqi success stories.
Such strikes on television stations in Belgrade during the Kosovo conflict had proved controversial, acknowledged the Tory leader, suggesting warnings could be given ahead of attacks.
In other developments:
British Army says southern port of Umm Qasr is now secure and humanitarian shipments could start within about 48 hours
Several hundred Royal Marines deployed along southern border with Iran, amid concerns fighters there could try to exploit uncertainty
Two British soldiers injured in battle have been flown to Birmingham's Selly Oak hospital for treatment
An ICM/Guardian newspaper polls suggest 54% of people approved of attacking Iraq to remove Saddam, with 30% against