U.S. combat troops mostly left Iraq's cities and towns by midnight on Tuesday and redeployed to rural areas until the end of 2011, six years after invading the country and eventaully overthrowing the previous government under its now executed president Saddam Hussein.

With Iraqi forces taking over most of the security, the government declared today a National Sovereignty Day holiday and held a military parade involving thousands of Iraqi soldiers and police in the fortified Green Zone government and diplomatic district, reported CNN.

Streets in Baghdad were empty as people feared to go outside their homes for fear of violence, the New York Times reported.

Four U.S. soldiers died today in Baghdad today, however, in what was described by the military as combat-related injuries with no further details given, CNN said.

General Ray Odierno confirmed the troops' exit.

A small number of U.S. forces will remain in the cities to train, advise ... and enable Iraqi security forces, he told journalists, according to CNN.

There were a handful of outposts in Baghdad, requested by Iraqi authorities that were manned by U.S. troops, with some U.S. armored vehicles near an entrance to the Green Zone and on an airport road, the New York Times reported.

Under a previous agreement, all U.S. troops, except for trainers and advisers will leave the country by the end of 2011.

At the request of Iraqi authorities, the American military has ordered soldiers to remain in garrison for a few days to let Iraqis demonstrate they are in control, the Times reported. The withdrawal process began several weeks ago, according to the report.

The New York Times Iraq