U.S. and Iraqi forces are tightening their grip around the Imam Ali Shrine in Najaf, which Shi'ite militiamen have occupied for the last 20 days.
Iraqi National Guardsmen took up positions just a few hundred meters from the shrine, using loudspeakers to urge radical cleric Moqtada al-Sadr's fighters to vacate the site or face attack.
Iraq's defense minister Hazim al-Shaalan told Al-Arabiyah television that "decisive hours are drawing near," but suggested a raid would not come Tuesday.
Earlier Tuesday, in Baghdad, insurgents separately targeted the convoys of the environment minister Mishkat Moumin and education minister Sami Mudhafar.
Neither official was hurt, but five bodyguards and a suicide bomber were killed.
A group linked to wanted terrorist Abu Musab al-Zarqawi claimed responsibility for the attack on the environment minister, saying it would not fail next time.
Information for this report is provided by AP, AFP and Reuters.