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The Bush administration is staying in close contact with Iraqis as they seek to wrap up writing a draft constitution, and are putting on a brave face through difficult challenges.

On Tuesday, Pentagon spokesman Bryan Whitman said Defense Department officials are confident that the remaining issues that delayed the completion of the constitution will still be resolved, saying all parties are still at the table. He characterized the process as one of compromise, cooperation and significant progress and said a one-week extension does not seem unreasonable.

White House officials said Tuesday that Bush has been getting regular updates on the developments in the constitution process. Aides say the president is encouraged by the fact that the Iraqis are still working on the document and have expressed a commitment to finish the process.

Still, the toughest part of the job is still to be completed, acknowledged State Department spokesman Sean McCormack, who listed a number of issues that will have to be worked out.

"There are going to be more ups and downs" in the extra week the Iraqis have given themselves to finish the job," McCormack said, pointing to the debate that needs to be completed on the roles of women and religion in the country's governance.

"We will do everything that we can, within the bounds of what they want, to help them get that done," he added.

Secretary of State Condoleezza Rice (search) spoke by telephone Tuesday with U.S. ambassador Zalmay Khalilzad (search) as he assisted the drafters, McCormack said. The United Nations is offering advice, as well, he said.

"This is the democratic process at work," he said. "And they have said that they intend to meet their deadline. We certainly support them in that."

Late Monday, President Bush complimented Iraqi drafters for making "substantial progress" on the constitution.

"I applaud the heroic efforts of Iraqi negotiators and appreciate their work to resolve remaining issues through continued negotiation and dialogue," Bush said in a statement released while he remained on a month-long vacation at his Texas ranch. "Their efforts are a tribute to democracy and an example that difficult problems can be solved peacefully through debate, negotiation and compromise."

As the midnight deadline approached in Iraq, lawmakers in the 275-member National Assembly approved a seven-day extension to finish up work on a draft constitution after Kurdish leaders asked for additional time.

"We have to remember this is an enormously important document and what you have here is people trying to build a common future after decades of tyranny," Rice said late Monday.

"They have achieved a lot and they have considerable momentum toward the completion of their constitution," she continued. "Iraqis have continued to demonstrate their commitment to a new Iraq based on the rule of law and their desire for a common future. We are witnessing democracy in Iraq."

Shiite, Sunni and Kurdish framers of the charter had reached a tentative deal late Monday, resolving issues ranging from oil revenues to the country's name but putting off decisions on the most contentious questions — including federalism, women's rights, the role of Islam, and possible Kurdish autonomy.

The Shiites are demanding that Islam be the main source of legislation. That could affect the civil code — because in Islamic law, or sharia (search), women might not receive the same share of inheritance and cannot initiate divorce.

Those demands are of concern to U.S. officials, who say they have made it clear that they expect women's rights to be protected in the constitution.

"We think it's very important that Iraq be for all Iraqis, an Iraqi democracy be for all Iraqis, men and women as well as different ethnic groups, different religious groups," McCormack said Monday. "And they should take that into account in the drafting of their constitution."

"If the new Iraq is going to go into the 21st century at all sensibly and begin to make a difference in terms of the Muslim world, they're going to have to face that women's rights issue and they're going to have to get it right … [they can't] go on treating them like second- or third-class citizens," former Secretary of State Lawrence Eagleburger (search) told FOX News.

When the constitution is written, the National Assembly will decide whether to give its approval. If it passes, Iraqis will vote around Oct. 15 to accept or reject the charter, leading to more elections in December for the country's first new government under the new constitution.

Administration officials have been quick to point out that delays are a part of the democratic process and consensus-building is as important as finishing the draft.

"Yes, there was an August 15 deadline to complete the constitution. There was also a way for them to avail themselves of a few more days and this is a very important process," Rice said.

"These people are working very, very hard, they have been working very long hours, and what that says is that they are really committed to putting together a document that they believe in, a document that can be a foundation for a free and democratic Iraq for all Iraqis, and that they are determined to do that," she said.

As remaining constitutional disputes are resolved the administration hopes minority Sunnis, who make up a significant core of the insurgency, will turn away from violence. Then, as Iraqi security forces improve, U.S. troops may begin to withdraw.

More than 1,800 American forces have died in Iraq since the U.S.-led invasion more than two years ago, and polls show public support for the war is dropping.

FOX News' Carl Cameron, Sharon Kehnemui Liss and The Associated Press contributed to this report.