US President George W. Bush's national security adviser Condoleezza Rice said on Tuesday that Iraq is not "falling into civil war," although the country faces a "very difficult situation."

"There's no evidence that the Iraqis are falling into civil war," Rice told NBC television's "Today" show, claiming progress is being made despite the recent wave of car bombings and hostage-takings.

"There's a political process underway in Iraq that has already brought into power a very good government," she insisted.

Rice expressed the belief that the Iraqi national elections slated for January will be held on schedule, stressing that the Iraqi people "have met every deadline that anyone put before them."

Insurgent violence in war-torn Iraq has been running rampant during the 18-month-old military occupation by US-led coalition troops.

At least 1,037 members of the US military have died in Iraq since the beginning of the Iraq war in march 2003, according to the US Defense Department.