US President Barack Obama hails the withdrawal of US forces from Iraqi towns and cities as a "milestone" but warns of the "difficult days" he believes are yet to come.

Obama late Tuesday touched on the US military success in meeting a June 30 deadline to complete its pullout from urban areas and hand over full control to local security forces ahead of its planned departure from Iraqi soil by 2012.

The president, however, acknowledged that "there will be difficult days ahead" and warned that there are "those who will test Iraqi security forces and the resolve of the Iraqi people through more sectarian bombings".

Obama advised leaders of the various Iraqi factions to make the needed "hard choices" to settle disputes and overcome obstacles to real political reconciliation.

On Tuesday, the Iraqi government marked the withdrawal with "a national day of sovereignty" inside the green zone where security forces jubilantly paraded with tanks and armored vehicles.

Iraqi celebrations, however, were marred as a car bomb hit a market in the oil-rich northern city of Kirkuk and killed at least 32 Iraqis and injured over 100 others.

The bombing, which was the latest in a wave of attacks that have claimed more than 250 lives in the past two weeks, came amid tight security and anticipation of horrific terrorist attacks amidst the pullback.

Iraqi Prime Minister Nuri al-Maliki has repeatedly warned that militant attacks are likely to rise in the coming weeks to "undermine confidence in Iraq's own security forces".

Maliki had earlier stressed his administration's determination to regain full sovereignty of the country despite "acts of terrorism".

US troops stationed in Iraq currently number around 131,000, many of whom will remain embedded among the Iraqi security forces.