Iraq's interim prime minister Iyad Allawi (search) said Saturday that national elections set for January 2005 could be delayed if security is not established in the volatile country.

Iraq's interim constitution says elections for a national assembly must be held by Jan. 31. But Allawi said in an interview with CBS News they could be delayed for up to two months.

"We are committed to elections and one of the tasks is really to work toward achieving these objectives," Allawi said in an interview in Baghdad with Dan Rather.

"However, security will be (the) main feature of whether we will be able to do it in January, February or March."

Asked if January was an "absolute certain date," for a vote, Allawi replied: "It's not absolute yet, it depends on how things will move. But we hope, and all of us will work toward that objective."

Allawi was appointed prime minister June 1, and his government is due to assume sovereignty from the U.S. occupation authority on Wednesday.

Iraq has been hit by a recent spate of car bombings and attacks that authorities blame on insurgents and supporters of Jordanian terrorist leader Abu Musab al-Zarqawi (search).

Allawi and members of his government have spoken in past days of possibly imposing martial law in some part of Iraq in an effort to rein in violence.

Allawi said in the interview that the government was considering law "that we are calling the defense of public safety" that would "empower the government to take action to defend its people."

"It wouldn't be martial law," he said. But it would allow the government to "take actions and measures against criminals, apprehend them, question them ... and impose curfews."

National elections are to be held in January to choose a national assembly, which would create a new government to replace Allawi's and would convene a national convention to draft a constitution that would be put to voters in October 2005.

Some fear postponing the January ballot could trigger unrest among the country's Shiite Muslims, who make up about 60 percent of Iraq's population. Shiites are expected to dominate any new elected government.

Changing terms laid down in the interim constitution could also further worry Iraq's Kurds (search), who have already expressed fears that constitutional provisions for their self-rule powers won't be respected.