The Iraqi Governing Council was dissolved Tuesday as a new president and prime minister took their positions in Iraq's government.

"We Iraqis look forward to being granted full sovereignty through a Security Council resolution to enable us to rebuild a free, independent, democratic and federal unified homeland," new President Ghazi Mashal Ajil al-Yawer (search) told a press conference.

New Prime Minister Iyad Al- Allawi (search) said Iraqis "are starting our march toward sovereignty and democracy."

In Washington, President Bush hailed the new government as a team that "represents the talent, commitment and resolve to guide Iraq through the challenges that lie ahead."

"The naming of the new government brings us one step closer to realizing the dream of Iraqis -- a fully sovereign nation with a representative government that protects their rights and serves their needs," Bush continued in the Rose Garden. "This is a very hopeful day for the Iraqi people … [and] for the American people."

Noting the recent terror attacks in Iraq, Bush said, "we will not be deterred by violence and terror and "we will stand with the Iraqi people."

The selection of al-Yawer to the largely ceremonial position broke a deadlock over the makeup of a new Iraqi government set to assume power June 30. Iraqi leaders said the Americans were trying to force them to accept the U.S.-backed candidate, former Foreign Minister Adnan Pachachi (search), although U.S. officials said they didn't push for one over the other.

"These are not America's puppets," National Security Adviser Condoleezza Rice told reporters at the White House. "This is a terrific list and really good government and we're very pleased with the names that emerged."

The Governing Council decided to dissolve immediately rather than remain in office until the transfer of sovereignty to the new government, said council member Younadam Kana.

The Coalition Provisional Authority would remain sovereign until June 30 to help the new leadership phase in. A senior Bush administration official also said the new Cabinet would begin negotiations on the status of U.S. and other coalition forces in Iraq after June 30 "fairly soon."

President Bush scheduled an 11:30 a.m. EST news conference in the Rose Garden to publicly comment on the event.

A senior Bush administration official said the White House was pleased with the selection of Allawi — a U.S.-backed Shiite Muslim with military and CIA connections — as prime minister and al-Yawer as president, despite reports that the Americans were pushing for Pachachi.

The official denied the United States had a favorite for the presidency, saying U.S. officials here "went back to Washington for guidance" and was told that "either of them would make an excellent president for Iraq."

"We lobbied for neither one," he said.

Iraqi officials had said Allawi was chosen because he was considered the best choice to cope with the deteriorating security situation.

"We're pleased that a number of qualified candidates were available for the top positions and I'm very pleased with the outcome," Secretary of State Colin Powell told reporters after a meeting with Georgia's leaders. "It's exactly what we wanted Mr. Brahimi to do."

U.N. envoy Lakhdar Brahimi offered "sincere congratulations and best wishes on the success of their mission."

"I think that the people of Iraq will be praying all over the country for the success of their mission, which aims at starting the rebuilding of the new Iraq," Brahimi said.

New Faces of Iraqi Leadership

Adil Abdel-Mahdi, an official of a powerful Shiite political party, was named finance minister; Hazem Shalan al-Khuzaei became defense minister; and Thamir Ghadbhan took over as oil minister. The two vice presidencies went to Ibrahim al-Jaafari, of the Shiite Muslim Dawa party, and Rowsch Shaways, speaker of parliament in the Kurdish autonomous region in Irbil.

Allawi later announced his Cabinet. Hoshyar Zebari retained his post as foreign minister and Kurdish official Barham Saleh, who is close to the Americans, was named deputy prime minister for national security affairs.

At the welcoming ceremony, al-Yawer pledged to rise "above sectarianism and divisions," build a democratic state free of "totalitarianism and discrimination" and restore Iraq's "civilized face."

He said he would be "a loyal defender of your expectations in restoring the complete sovereignty of our country and establishing a democratic and federal system under which people enjoy a free citizenship in a state of laws and freedom."

Allawi also said Iraq needs help from U.S. and other multinational forces to help defeat "the enemies of Iraq." The statement was seen as a prelude to the new government negotiating an agreement that would allow troops of the U.S.-led coalition to continue operating in the country.

In a nod to U.S. forces, al-Yawer said "we should remember our friends who fell during the battle to liberate Iraq." He has denounced violence against American and other coalition forces.

The new Minister of Industry, Hajim al-Hassani, told Arabic satellite news station Al-Jazeera that as of Wednesday there would be "no more American coordinators to impose their will on Iraqi ministries."

"The ministries can make use of their available expertise but the final decision will be an Iraqi one," he said.

The next Iraqi government must negotiate the legal basis under which the 135,000 American troops and other coalition forces will remain under a sovereign Iraqi government.

New Government Works to Defeat Terrorism

"I think it's been a good day for the Iraqi people," Powell said. "There are still those terrorists trying to keep the Iraq people from democracy and freedom but we've determined they will be defeated."

As word of al-Yawer's appointment was announced, a car bomb blew up outside the offices of the Patriotic Union of Kurdistan, which is located just outside the green zone headquarters of the U.S.-run coalition in central Baghdad.

Initial reports indicate that two Iraqis were killed and 27 wounded. One Iraqi was also wounded in several rocket attacks on the Green Zone that began around 12:15 local time.

"This is a very miserable day for the terrorists … terrorism cannot live with democracy, that's why they have tried to derail the democratic process," Mowaffak Al-Ribaie, Iraq's new security adviser, told Fox News, adding the economic reconstruction in Iraq, as well as preparing the country for next year's elections, are also priorities of the new government, alongside getting rid of terrorism.

Adding the involvement of the United Nations "will give this government legitimacy," Al-Ribaie said he believes Iraqis will take the new government seriously.

Brahimi had hoped to complete the selection of the 26-member Cabinet by Monday, but the dispute over the presidency delayed the decision for a day.

Most of the 22-member Governing Council backed al-Yawer, the current council president. A graduate of the Petroleum and Minerals University in Saudi Arabia and of Georgetown University, he is a prominent member of the Shammar tribe, one of the largest in the Gulf region that includes Shiite clans. He enjoys the support of Shiite and Kurdish council members.

Ahmed Pachachi, a relative and an aide to Pachachi, said the 81-year-old former minister was offered the presidency but turned down the post.

Adnan Pachachi later told reporters that the president "must have the support of all levels of the Iraqi people and all quarters." He denied that he was the coalition's choice.

"I apologize (for turning down the job) for valid reasons and for personal reasons," he said.

In Mosul, al-Yawer's hometown, crowds swept into the streets to celebrate the news, cheering and firing weapons in the air. American soldiers there appealed for calm.

Fox News' Dan Springer and The Associated Press contributed to this report.