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British Prime Minister Tony Blair agreed with Iraq's new leadership Monday that Iraqi security forces would start assuming full responsibility for some provinces and cities next month, beginning a process leading to the eventual withdrawal of all coalition forces.

Blair and Iraqi Prime Minister Nouri al-Maliki declined to set a timetable for that withdrawal, but British media quoted an unidentified senior British official traveling with Blair as saying coalition forces should be out within four years.

CountryWatch: Iraq

The British and Iraqi leaders said "responsibility for much of Iraq's territorial security should have been transferred to Iraqi control" by December. At that point, al-Maliki said, two of Iraq's most violent provinces, Baghdad and Anbar, may be the last where coalition forces maintain control.

However, handing over security responsibilities to the Iraqis does not necessarily mean that significant numbers of U.S.-led forces will start returning home soon. Instead, plans call for them to move from cities to large coalition bases as part of an intermediate stage — where they will be on call if the Iraqis need them.

"It has been longer and harder than any of us would have wanted it to be, but this is a new beginning and we want to see what you want to see, which is Iraq and the Iraqi people able to take charge in their own destiny and to write the next chapter of Iraqi history themselves," Blair said in the first visit by a foreign leader since al-Maliki's government took office Saturday.

Blair now heads to Washington for talks with President Bush that likely will focus on their overall strategy in Iraq.

In Chicago, Bush acknowledged to war-weary Americans that the situation in Iraq is improving only gradually, and he urged patience with "more days of challenge and loss."

Bush has refused to put a timetable on an American withdrawal, saying in March that American forces would remain in Iraq for years and a future president would decide when to bring them all home.

The United States has 132,000 service members in Iraq, while Britain has about 8,000. Like Bush, Blair has seen his public support fall because of opposition to the Iraq war.

On Monday, Blair and Iraqi al-Maliki issued a joint statement saying Iraqi forces would begin in June "progressively and quickly taking on full responsibility for security from multinational forces in the cities and provinces of Iraq."

As they spoke, the relentless violence killed at least 20 people, most of them in the capital. The U.S. military said a Marine was killed in combat Sunday.

Blair's official spokesman said at a news conference in Baghdad that he could not confirm the media report of a withdrawal within four years. Blair and al-Maliki also declined to set any deadline, with Blair saying withdrawal depends on the "readiness of the Iraqi troops and the situation on the ground."

On Jan. 31, a U.S. Embassy report found security "critical" in Anbar province, the Sunni-dominated region that includes war-torn Ramadi and Fallujah and is where many of the Sunni Arab-led insurgent groups are based.

The U.S. military said a U.S. Marine was killed in action in Anbar province Sunday. At least 2,457 U.S. service members have been killed since the war began, according to an AP count.

The security situation was considered serious in the provinces of Baghdad, Basra, Ninevah, Tamim, Salahuddin and Diyala — all of them religiously mixed between majority Shiites and minority Sunni Arabs. Those provinces include Iraq's three largest cities and the bulk of its oil wealth.

On May 6, a British military helicopter crashed — it apparently was shot down — and all four soldiers aboard it died. Some Iraqis celebrated and in fighting that followed between British forces and Shiite gunmen, five Iraqis were killed.

Blair and al-Maliki discussed the situation in Basra on Monday and agreed to send a high-level Iraqi delegation soon to improve security and stability there.

In their joint statement, Blair and al-Maliki said the new government's plan is to have 325,000 members in Iraq's security forces by the end of the year, compared with 264,000 currently serving in the army and police forces.

Al-Maliki's new national unity government was sworn in Saturday and the prime minister pledged to used all means necessary — including "maximum force" against insurgents, "death squads" and some militias — to restore stability and security.

Blair said Iraq's first full-term democratic government means there is no longer any justification for insurgents and that the best way for militants to get foreign troops to leave Iraq would be to lay down their arms.

"If the worry of people is the presence of the multinational forces, it is the violence that keeps us here. It is the peace that allows us to go," Blair said.

Separately, Iraq's Sunni Arab vice president said Iraqis had a legitimate right to resistance until coalition forces left Iraq. But Tariq al-Hashimi also called on insurgents to consider sitting down and talking to the United States since America was apparently seriously thinking about eventually withdrawing its forces.

Asked if Blair had spoken with Bush before traveling to Iraq, the prime minister's spokesman said the two leaders often talk regularly and "know each other's minds about Iraq."

The official, who spoke on condition of anonymity according to British government policy, also said Blair used his one-day visit to Baghdad to meet with U.S. Ambassador Zalmay Khalilzad and the top U.S. commander in Iraq, Gen. George Casey.

During the news conference, al-Maliki was asked whether the surge in sectarian violence in Iraq, which has prompted thousands of Iraqis to flee their homes, is a civil war.

"There are rebellious elements. There are gangs killing people. There are gangs that have used arms for political blackmailing or to achieve goals that have political dimensions," he said.

"But those groups have failed to ignite a civil war because the political, religious and social groups have faced this plot."

In Monday's deadliest attack, a roadside bomb killed four policemen in Musayyib, about 40 miles south of Baghdad, police said. Car bombs in two areas of the capital killed nine Iraqis and wounded 13, police said.

Elsewhere, officials said gunmen killed a police colonel in Samarra; an employee of a mobile phone company in Baqouba; the general director of the youth ministry in Baghdad; a Sunni Arab who headed the office that issues national ID cards to Iraqis in Kirkuk; and a former member of Saddam Hussein's Baath Party in Mosul.

Police found the bodies of two men — a police captain in the capital and a man in the Madain area, southeast of Baghdad — who had been shot in captivity.