Secretary of State Condoleezza Rice (search), on a surprise visit to Iraq Sunday, said the country can only succeed as a "unified Iraq" and re-iterated that the next step in the democratic process is to draft a constitution representative of the different ethnic groups in the country.

"The Iraqis are making enormous progress and they are to be congratulated for that," she told FOX News in an exclusive interview live from Iraq.

Rice praised ethnic and religious groups for their cooperation and urged patience as the country's elected government takes over. She also stressed the need to engage the country's Sunni population in the democratic process, saying that they are currently under-represented because they did not participate as widely in the election as other groups.

"The political way is the only path to a better future," she told FOX.

Rice met with leaders including Prime Minister Ibrahim al-Jafaari (search) and Deputy Prime Minister Ahmed Chalabi (search), the former Bush administration favorite who fell out with Washington before the January elections.

Rice pointed out that it has been less than one year since Iraqis assumed sovereignty and only weeks since the elected government was formed.

"Things do not happen overnight," Rice said, with al-Jafaari at her side. "We have become very impatient."

During her interview with FOX, the secretary of state acknowledged that the insurgency remains an on-going challenge to the political process, but said that by maintaining political momentum, continuing to make progress in restoring the country's infrastructure and by training Iraqi security forces, the country will continue to move toward independence.

"We would like nothing better than to have Iraqis capable of defending themselves," Rice told FOX News.

Rice also spoke to uniformed troops and U.S. Embassy employees in the fortified Green Zone (search) in the capital.

"We are so grateful that there are Americans willing to sacrifice so the Middle East will be whole, and free and democratic and at peace," she told several hundred people packed into a former Republican Palace that is now part of the embassy complex.

Rice's first stop was in Salahuddin, in Kurdish northern Iraq. She appealed for patience for the fragile government and said Iraqis have made remarkable political progress that can overcome a recent surge of violence.

Later, she flew in a military helicopter under heavy security to the mountain stronghold of Kurdish Democratic Party leader Massoud Barzani.

The one-day trip was Rice's first visit to Iraq as the nation's top diplomat.

Rice was a chief architect of the U.S.-led invasion of Iraq as White House national security adviser during President Bush's first term. She accompanied Bush on his own surprise visit to Iraq on Thanksgiving Day 2003.

She said she wanted to discuss the government's upcoming tasks including writing a constitution, as well as addressing security and infrastructure needs.

Rice told reporters that the August deadline to write a federal constitution was imposed by the Iraqis, not the United States. The continuing political situation and security challenges in Baghdad have complicated the process. Some in the Iraqi government now say that deadline may not be realistic.

"There needs to continue to be some momentum in the political process," Rice said after meeting with Barzani.

The visit came as U.S. Marines wrapped up a weeklong campaign against insurgents along the Syrian border. It was the most intense fighting for U.S. forces in months.

"Yes, the insurgency is very violent, but you can beat insurgencies not just militarily," Rice said en route to Iraq. "You can beat them having a political alternative that is strong," and in which all Iraqis are invested, Rice said.

Rice was the first senior American official to visit Iraq since the new government was sworn in. Her trip was weeks in the planning, but kept secret even from top State Department officials until the last minute.

Most Iraqi officials learned of the visit only hours before Rice landed in the region aboard a borrowed government plane, said a senior adviser to Rice, Jim Wilkinson.

Rice rejected any assertion that the tight security reflects poorly on the success of the U.S. led effort to rebuild Iraq after ousting Saddam Hussein two years ago.

"It says there are terrorists and old Baathists who want to destroy the seeds of democracy in Iraq and the seeds of democracy in the Middle East, that's what it says," Rice said.

Rice had canceled an earlier planned trip when word got out. This time she traveled with a much smaller contingent than usual. It included just three reporters.

A surge of militant attacks has killed at least 430 people across Iraq since April 28, when the country's first democratically elected government was announced.

U.S. military officials have urged al-Jafaari to act quickly to avoid a loss of confidence and goodwill among Iraqis.

"It's very hard what the Iraqis are being asked to do which is cast off years and years of tyranny and dictatorship and come to political unity in what is a very complicated place," Rice said.

"I think it's quite remarkable what they've done," so far, she said.

FOX News' Rick Folbaum and the Associated Press contributed to this report.