Baghdad, Iraq ? 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.

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.

British Prime Minister Tony Blair, center, walks with Iraqi President Jalal Talabani, second from left, on his arrival in Baghdad, Iraq. Blair on Monday became the first world leader to visit Baghdad since the new government took office Saturday. The visit was aimed at shoring up international support for the government as it comes to grips with the security crisis.

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.

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 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.