Iraq has become the "crucible of global terrorism", but insurgents will be defeated, Tony Blair has pledged.
Sunday is the first time the two leaders have met
Speaking after talks at Downing Street with Iraq's interim prime minister, he vowed to see the "struggle" through and deliver a "huge defeat" for terrorists.
Iyad Allawi called on the UN to provide whatever help was needed to make next January's planned elections a success.
He said he was adamant democracy would prevail against the "forces of evil" operating in his country.
"We definitely are going to stick to the timetable of elections in January next year," he told reporters on Sunday.
"We are succeeding in Iraq. We are succeeding against the forces of evil."
The UK prime minister said: "Now is not the time for the international community to divide or disagree but to come together.
"Whatever the disagreements about the first conflict in
Iraq to remove Saddam, in this conflict now
taking place in Iraq, this is the crucible in which the
future of this global terrorism will be determined.
"And either it will succeed and this terrorism will grow,
or we will succeed, the Iraqi people will succeed, and this
global terrorism will be delivered a huge defeat."
The Iraqi people's "struggle... is actually our struggle too, which is why we will see it through until it finishes - not in the victory of America, Britain or the West but the victory of the Iraqi people", Mr Blair added.
He praised Mr Allawi's courage and said they wanted to
see a free Iraq committed to stability, democracy, human rights and equality.
"The people who are trying to stop that Iraq coming about, who are engaged in killing, maiming and acts of terrorism, are people who are
opposed not just to the new Iraq that can take shape, but are opposed to every
single one of the values that we in countries like this hold dear.
"The terrorists who are conducting this killing in Iraq, they know what is at
stake. And we should know what is at stake as well."
Mr Allawi is visiting the UK as part of a tour which will also take him to New York and Washington.
The talks come as UK and US officials are working to secure the release of Briton Kenneth Bigley and Americans Jack Hensley and Eugene Armstrong, who were seized on Thursday from a house in Baghdad's Mansour neighbourhood.
They are being held by captors reportedly allied to al-Qaeda militant Abu Musab al-Zarqawi.
Mr Blair said he and Mr Allawi had
discussed Mr Bigley's situation.
"Our governments are working closely on it," he said.
"I don't think there's anything more I can or should say at this stage."
Mr Allawi added: "We are trying our best working on the
issue of hostages, and hopefully we will achieve some good results."
Earlier, Iraq's foreign minister told BBC One's Breakfast with Frost his government would not bow to the demands of the kidnappers.
Hoshyar Zebari, in London with Mr Allawi for the talks, said that would set "a very bad precedent".
It has been a week of intense violence in Iraq, with 23 killed in a bomb in Kirkuk on Saturday and 47 killed in a Baghdad blast earlier in the week.
Sunday is the first opportunity the UK prime minister has had to meet Mr Allawi since he was appointed in May.