Updated

A series of coordinated car bomb attacks on Monday killed 34 people, excluding the homicide bombers, in Baghdad, shattering what should have been a solemn day as Iraq began observing the Muslim holy month of Ramadan.

About 12 people were killed at the International Committee of the Red Cross (search) building in central Baghdad and 27 others were slain in attacks on three police stations. Most of the victims were Iraqis. The U.S. military said one American soldier was killed in one of the police station attacks.

Around 10:30 a.m. EST, Reuters reported that new explosions could be heard in central Baghdad.

Meanwhile, in Fallujah, 40 miles west of Baghdad, witnesses said U.S. troops opened fire, killing at least four Iraqi civilians, after a roadside bomb exploded on a U.S. military convoy.

Brig. Gen. Ahmed Ibrahim, the deputy interior minister, put the Iraqi death toll at 34, including 26 civilians and eight police but not the bombers. Iraq's police chief and deputy interior minister, Ahmad Ibrahim, told a news conference that 65 policemen and 159 civilians were also wounded.

One American soldier was killed in one of the police station attacks and six U.S. troops were wounded.

"There are terrorists in Iraq who are willing to kill anybody in order to stop our progress," President Bush told reporters Monday after meeting with U.S. military commander Gen. John Abizaid, Defense Secretary Donald Rumsfeld and L. Paul Bremer, the U.S. civilian administrator in Iraq. "The more successful we are on the ground, the more these killers will react. Our job is to find them and bring them to justice."

Bush said that the Iraqi people cannot let the small number "of killers willing to kill innocent Iraqis" to determine how they live in their own country, especially when a majority of Iraqis "want to live in a peaceful and free world."

Of the homicide bombers and terrorists in Iraq, Bush added: "We will find these people and we will bring them to justice … it's in the national interest of the United States that a peaceful Iraq emerges. We will stay the course to make sure we reach that objective."

The bloody bombing attacks came hours after clashes in the Baghdad area killed three U.S. soldiers overnight, and a day after insurgents devastated a hotel full of U.S. occupation officials with a rocket barrage, killing a U.S. colonel and wounding 18 other people. U.S. Deputy Defense Secretary Paul Wolfowitz was in the hotel, but was unhurt.

Defense officials said they believe loyalists of fallen Iraqi President Saddam Hussein were responsible for the wave of bombings, which showed some level of coordination.

In Baghdad, top Iraqi and U.S. officers blamed "foreign fighters," not Saddam diehards, for the day's mayhem. "That's a reasonable supposition," said U.S. Brig. Gen. Mark Hertling.

'We Feel Helpless'

It was two days of violence unprecedented in this city of 5 million people since the end of the U.S.-Iraq war last April.

"We feel helpless when we see this," a distraught Iraqi doctor said at the devastated Red Cross offices.

Witnesses said a homicide bomber drove an explosives-packed ambulance up to the ICRC building's security barriers around 8:30 a.m. and detonated it, blowing down the front wall, devastating the interior and blowing shrapnel and debris over a wide area.

Explosions then went off at the al-Baya'a, al-Shaab and al-Khadra police stations.

"From what our indications are, none of those bombers got close to the target," Hertling said.

Officers stopped a fifth would-be homicide bomber at another police station in central Baghdad before he detonated his Land Cruiser. "He was shouting, 'Death to the Iraqi police! You're collaborators!"' said police Sgt. Ahmed Abdel Sattar.

Ibrahim said the fifth would-be bomber was captured with a Syrian passport.

"Some countries, unfortunately, are trying to send people to conduct attacks," he said.

Red Cross Disaster Area

The Red Cross said 12 Iraqis were killed at its office, including two of its own employees.

In Geneva, Red Cross spokesman Florian Westphal said the ICRC had disclosed in August that it had received warnings of a threat and added that it had been cutting back on its staff since a Sri Lankan staffer was killed July 22 south of Baghdad.

"Such an attack is a major blow for us," Westphal said. "It's a big shock. It is obviously impossible to move onto a normal day's business, so we really have to step back and take stock."

Cigarette vendor Ghani Khadim, 50, said he saw an Iraqi ambulance approach the small ICRC compound some 100 yards away. It suddenly exploded and the blast blew out windows and injured his wife and daughter in his house behind his stand.

The blast blew down a 40-foot section of the ICRC front wall, demolished a dozen cars in the area and apparently broke a water main, flooding the streets. The building's inside was heavily damaged.

"Of course we don't understand why somebody would attack the Red Cross," said Baghdad ICRC spokeswoman Nada Doumani.

The explosion devastated the interior of the nearby Al-Nawal private polyclinic operated by Dr. Jamal F. Massa, who had been planning to open it as a full-fledged hospital next month.

"This only hurts guards and other Iraqis," Massa said.

ICRC and other international aid organizations had reduced their Baghdad staffs after the car bombing of U.N. headquarters in Baghdad on Aug. 19, in which 23 people died.

Police Station Bombings Kill 27

Police said 27 were killed in the police station bombings, most of them Iraqis, 15 of whom were killed at the al Baya'a station in the ad-Doura district.

The station had been open only a month and was jointly staffed by Iraqis and Americans. The attacker drove up to the station in a vehicle disguised as a police truck, which detonated and blew down the building's front wall.

Hertling said Monday was "a great day for the Iraqi police" because security controls prevented the bombers from reaching their targets.

But Mouwafak al-Rabii, a Shiite Muslim member of the U.S.-appointed Iraqi Governing Council, said the United States must speed up the training of Iraqi police and soldiers and employ ruthless measures to crush the insurgency.

"There is no doubt about it that we need to change the rules of engagement with these people," al-Rabii said in a television interview. "The rules of engagement now are too lenient."

The Hunt for Saddam

Maj. Gen. Ray Odierno (search), commander of the 4th Infantry Division in northern Iraq, told reporters that the hunt for Saddam is still centered in his area of operation, and 'human' intelligence in Tikrit and its surrounding areas still indicates Saddam is still moving around his ancestral home.

Odierno believes Saddam is not demonstrating any significant amount of control over the clusters of regime loyalists that continue to harass U.S. forces.

Odierno also said that coalition forces in the north are seeing little evidence of coordination between foreign fighters and regime loyalists, speculating that a the new uptick in attacks on coalition facilities and patrols is the work of loyalists who are "desperate" because they see the coalitions stabilization efforts "working."

Operation Ivy Focus (search), designed to take Saddam loyalists off the street and deny them access to money and weapons, continues to produce promising results, Odierno said. The Task Force Iron Horse (search) operation, which kicked off Sept. 10, has netted 123 "mid-level" loyalists, 43 makers of improvised explosive devices, six financiers and $1.5 million.

Fox News' Bret Baier, Ian McCaleb and The Associated Press contributed to this report.