Under tight security in Baghdad, US Marines have raised their flag over the world's largest American embassy.

During an inauguration ceremony on Monday, US officials said the $700m state-of-the-art complex will usher in a new era of relations with Iraq, which it invaded nearly six years ago.

The ceremony was held a day after a suicide bomber killed at least 38 people at a Shia shrine just 6km north of the new embassy.

On Monday, four bombs went off in different parts of Baghdad just before noon, killing four people and injuring 19 others.

Last week, the Green Zone -- the walled-off swath of central Baghdad -- was formally turned over to the Iraqi government, whose authority the US military will now operate under, according to an agreement that took effect on January 1.

"Iraq has now assumed the lead for all security operations and our bilateral relationship going forward will be governed" by the agreements, Ryan Crocker, US ambassador to Iraq, said.

"Iraq is in a new era and so is the Iraqi-US relationship."

Although it will maintain its independent chain of command, the US will be subject to Iraqi laws under certain conditions.

The accord also allows US troops to play an advisory role to the Iraqi military as they prepare to pull out of Iraqi cities in June and before leaving entirely at the end of 2011.

US diplomats and military officials moved into the embassy, which at 42 hectares is the size of 80 football fields, on December 31 after vacating Saddam Hussein's Republican Palace, which they occupied after capturing Baghdad in April 2003.

'Fortress-like'

During Monday's ceremony, Jalal Talabani, Iraq's president, praised George Bush, the US president, for invading Iraq in 2003 and toppling the regime of Saddam, who was executed two years ago.

"The building of this site would not be possible without the courageous decision by President Bush to liberate Iraq," Talabani said. "This building is not only a compound for the embassy but a symbol of the deep friendship between the two peoples of Iraq and America."

The new embassy, which was originally slated to open in September 2007, has been criticised for shoddy building practices. Some have also questioned the fortress-like building's "bunker mentality".

"What kind of embassy is it when everybody lives inside and it's blast-proof, and people are running around with helmets and crouching behind sandbags?" Edward Peck, a former American diplomat in Iraq, asked in 2006.

One US official said the cost of running the new complex is expected to be so exorbitant that the US will be forced to rent out part of the space.