"We have reached an agreement. There is going to be very good news very soon," Mowaffaq al-Rubaie, a Shia on the 25-member Council, told reporters after emerging from half an hour of talks with Ayatollah Ali al-Sistani, a reclusive cleric who wields huge influence among Iraq's Shia majority.

"We are going to sign (the interim constitution) Monday."

It was not immediately clear if Rubaie meant that Sistani had accepted the existing wording of the interim constitution, which was agreed to by the Governing Council last week, or if he had worked out changes to the wording with Sistani that would then have to be presented to the rest of the Council.

The interim constitution is crucial to US plans to hand power back to the Iraqis at the end of June.

The US-appointed Council was due to sign the constitution last Friday, but at the last minute five Shia members refused to sign after it emerged that Sistani, a 73-year-old Iranian- born cleric, had objections to two key clauses in the document.

One objection referred to a clause that would give the Kurds, who make up about a fifth of Iraq's population, an effective veto over the permanent constitution once it is drawn up after elections next year.

Another involved the make-up of a presidential council. Currently the document calls for the creation of a three-member council, with one president and two deputies. Shias have said they now want a five-person council, with three Shias, one Sunni and one Kurd.

Earlier a delegation from Iraq's Governing Council met aides to the country's top Shia cleric on Saturday to try to salvage a deal on an interim constitution crucial to US plans to hand power back to Iraqis.

In Crawford, Texas, President Bush vowed to crush militants behind attacks this week that killed at least 181 people in Baghdad and Kerbala, and signaled a major push against chief suspect Abu Musab al-Zarqawi.

Bush offered his first personal response to Tuesday's bomb attacks on Shia worshippers.

"Laura and I and the American people were filled with grief and anger at these terrible attacks of murder," he said. "We will defeat the terrorists who seek to plunge Iraq into chaos and violence, and...stand with the people of Iraq for as long as necessary to build a stable, peaceful and successful democracy."

The US Army said its troops had fired on a truck rigged with explosives in the "Sunni triangle" west of Baghdad on Saturday. The driver was killed and three US soldiers were wounded.