Saudi security officials said four of its forces died in the clash and the Interior Ministry said three of the five attackers were killed. The other two were injured and captured in the first militant assault since May. Five members of the consulate's non-American staff died, according to the U.S. Embassy.
One American was slightly injured, apparently while being evacuated, a State Department official said in Washington, speaking on condition of anonymity.
During the battle, "gunships hovered overhead, huge plumes of smoke were seen all over the city, fire broke out, ambulances rushed to the scene," Global Radio News reporter Phil Moore told CBS Radio News.
President Bush said the attack showed "terrorists" are trying to intimidate Americans and force the United States to withdraw from Saudi Arabia and Iraq.
"They want us to grow timid and weary in the face of their willingness to kill randomly, kill innocent people," Mr. Bush said at the White House after a meeting with interim Iraqi President Ghazi al-Yawer. "That's why these elections in Iraq are very important."
Mr. Bush also thanked Saudi Arabia for quelling the attack and said more would be learned about who was behind it.
A non-American employee of the consulate said staff was moved to a safe area inside.
In Riyadh, U.S. Embassy spokeswoman Carol Kalin said four of the five employees killed held administrative jobs and one was a private contract guard on the consulate's payroll. Four other embassy workers — all hired locally — were hospitalized, Kalin said. She said all American employees were safe and none had been taken hostage.
Kalin said it was unclear if any of the U.S. Marine guards inside the consulate were involved in the gun battle.
"We have accounted for all Americans on the compound in Jiddah and none of them are being held hostage," Kalin said.
As a precaution, she said, the U.S. Embassy in Riyadh and consulate in Dhahran were closed to the public through Tuesday, with only emergency services available for American citizens, according to a statement posted by the U.S. Embassy after the attack. It urged Americans living in Saudi Arabia to "exercise utmost security precautions."
The attack has the State Department alarmed, says CBS News Reporter Charles Wolfson.
"The whole system is designed to prevent this from happening," said one senior State Department official, calling the attack on the consulate a "major breach of security measures."
According to this official, "there is concern now that defensive measures the State Department has in place all over the world ... proved vulnerable."
Additional diplomatic security personnel are being sent to Saudi Arabia, both to bolster current levels of security at American diplomatic posts and to help in the investigation in Jiddah.
"It has taken the city of Jiddah by surprise, because this is a very serious incident and of a magnitude that we did not expect," Arab News editor-in-chief Kahlee el Maeena told CBS Radio News.
The statement by a Saudi Interior Ministry spokesman, carried by the official Saudi Press Agency, said a "deviant bunch" — a reference to Islamic militants — threw explosives at the gate of the consulate, then entered. Saudi security forces engaged the attackers, "killing three aggressors, and two were captured after they were hit," the statement said.
"The situation was brought under control," the statement said. It gave no further details.
The Saudi official in Riyadh said the gunmen got to an area inside the initial security gate at the consulate compound, but outside a secondary gate that protects the consulate offices.
Area residents spoke of seeing Saudi forces enter the consulate, located inside a compound surrounded by walls at least 10 feet high and topped with barbed wire, shortly before the fierce gun battle was heard inside. Soon after, the gunfire stopped.
"They were very, very professional in the way they handled things. They were carrying heavy weapons and [an eyewitness] said they were wearing body armor," Arab News reporter Roger Harrison told CBS News. "This would indicate that maybe there's been some very serious training going on."
There was no immediate claim of responsibility. But Saudi officials have blamed al Qaeda operatives for the string of attacks that have hit the kingdom in the past two years.
On Islamic militant Web sites, contributors began hailing the attack even before it was over, with one person praising it as "destruction of a bastion of atheism."
"We were afraid about our brothers in the Arab peninsula, but this proves that they are well and sound, thank God," said the person who made the posting, referring to recent Saudi crackdowns on militants.
The consulate — like all U.S. diplomatic buildings and other Western compounds in Saudi Arabia — has been heavily fortified and guarded since last year's series of bombings against targets housing foreigners. Guard posts are located on the corners of the compound and a road open to civilian traffic runs along part of the wall.
"The magnitude of this assault on the consulate has taken all Jiddah residents by surprise," said Khaled al-Maeena, the editor of Arab News located in Jiddah who saw the smoke rising from the compound.
The series of attacks on Western targets in Saudi Arabia started in 2003, when car bombs targeted three compounds housing foreign workers in Riyadh, killing 35 people, including nine suicide bombers.
About 9,000 Americans live in the Jiddah consular district, which encompasses western Saudi Arabia from Yemen to Jordan. The population of Jiddah is estimated at more than 2 million.