Insurgents are losing their struggle to destabilise Iraq's interim government, its prime minister insisted ahead of his first talks with Tony Blair.
Iyad Allawi is also flying to the US
Iyad Allawi is meeting Mr Blair at Downing Street, for talks expected to discuss security in Iraq and Thursday's kidnapping of a Briton.
Mr Allawi blamed continuing violence on foreign extremists, who, he told US TV, had mobilised disaffected Iraqis.
But he said they were not getting stronger, but more desperate.
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.
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".
Mr Blair and Mr Allawi will also discuss growing concerns about whether Iraq will be able to hold planned elections in January.
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.
The meeting was intended to be a review of progress in Iraq.
But after the tragedies of the last week, it is likely to be largely dominated by immediate security issues.
Mr Blair will also want to discuss whether it is possible to advance the Iraqi political process, by getting more people involved in politics, in the current climate.
On Saturday, the prime minister tried to play down reports that he had been warned that Iraq was likely to descend into chaos, a year before the war.
"Having read in the papers that apparently I was warned of the chaos that was going to ensue in Iraq, I actually got the minute Jack sent me. It didn't do anything of the sort.
"What it warned of was this - it's very important that we don't replace one dictator, Saddam Hussein, with another.
"The idea that we did not have a plan for afterwards is
simply not correct. We did, and we have unfolded that plan, but there are people in Iraq who are determined to stop us."
He said Iraq was "the very crucible of the fight against terrorism, against groups that are prepared to kill, or take hostages, or do whatever they can in order to prevent Iraq becoming a stable, democratic country".