More than 1,000 U.S. troops and Iraqi forces on Tuesday launched Operation Sword (search) in an effort to defeat terrorists and foreign fighters in western Iraq (search).

Operation Sword marks the third major offensive in the area in recent weeks as coalition and Iraqi forces attempt to quash an insurgency that's aiming to derail the democratic progress of the fledgling government.

The insurgency has killed more than 1,350 people — mostly civilians and Iraqi security forces — since Prime Minister Ibrahim al-Jaafari (search) formed his Shiite-dominated government on April 28.

Meanwhile, a homicide car bomb killed a Shiite legislator and three others near Baghdad (search) on Tuesday, an attack likely to further fuel ethnic tensions on the one-year anniversary of the transfer of sovereignty to Iraqi authorities.

A U.S. soldier part of Task Force Liberty was also killed when a car bomb detonated near a coalition forces base near Balad around 11:40 a.m. June 28. The name of the soldier is being withheld pending notification of next of kin. One wounded soldier was taken to a coalition medical facility for treatment of non-life-threatening wounds.

President Bush on Tuesday will try to ease Americans' doubts about the mission and outline a winning strategy for a conflict that has cost the lives of more than 1,740 U.S. troops.

In a prime-time address from Fort Bragg, N.C., home of the Army's elite 82nd Airborne Division, Bush was to argue that there is no need to change course in Iraq despite the upsetting images produced by daily terrorist attacks.

Watch FOX News Channel at 8 p.m. EDT to watch President Bush's live address.

Although attacks frequently take the lives of American troops, Bush has said they will not leave until Iraqi security forces are trained and equipped to keep the peace. He has refused to give a timetable for troop withdrawal, even though some Democrats and a few Republicans in Congress are supporting a resolution that calls for Bush to start bringing them home by Oct. 1, 2006.

In the homicide bombing Tuesday, National Assembly legislator Dhari Ali al-Fayadh and his son were killed in the homicide attack while traveling to parliament from their farm in Rashidiya, 20 miles northeast of Baghdad, said parliamentarian Hummam Hammoudi, who heads a committee charged with drafting a new constitution.

Two of al-Fayadh's bodyguards were also killed, and four were wounded, police Maj. Falah al-Mihamadawi said.

Al-Fayadh was a senior sheik from the al-Boamer tribe in the Mahmoudiya area, about 20 miles south of Baghdad and a hotbed of the Sunni-dominated insurgency. Al-Boamer includes both Sunni and Shiite clans.

"Those who killed the sheik are the enemies of the Iraqi people at large," Hammoudi said.

Al-Fayadh, in his late 80s, was the eldest member of the new parliament that was installed about three months ago and he had acted as speaker until one was elected. He was a member of the country's largest Shiite political party, the Supreme Council of the Islamic Revolution in Iraq.

Al-Fayadh was the second Shiite legislator to be killed since the new parliament started work in March. Lamia Abed Khadouri al-Sagri was killed April 27 in eastern Baghdad. She was a member of the Iraqi List party.

The country's Shiites are already on edge following a series of car bombings last week that killed nearly 40 people in predominantly Shiite neighborhoods in Baghdad. With the Sunni Arab-dominated insurgency targeting the Shiite majority, the wave of killings has raised fears of civil war.

Elsewhere on Tuesday, a homicide car bomber slammed into a convoy carrying Kirkuk traffic police chief Brig. Gen. Salar Ahmed, killing one of his bodyguards and a civilian in the northern city, police Lt. Assad Mohammed said. Four were wounded, including Ahmed and three of his bodyguards. Kirkuk is 180 miles north of Baghdad.

The new U.S.-led military campaign is focusing on communities along the Euphrates River between the towns of Hit and Haditha in the volatile Anbar province, said Marine Capt. Jeffrey Pool, a spokesman. The U.S. troops include Marines, soldiers and sailors from Regimental Combat Team 2, which is part of the 2nd Marine Division.

The region, about 125 miles northwest of Baghdad, is a hotbed of terrorist activity. Operation Sword, or Saif in Arabic, comes on the heels of two other offensives — dubbed Operations Spear and Dagger.

Operation Spear was aimed at stemming the flow of foreign fighters over the porous Syrian border in Karabilah, which is near the Iraqi frontier town of Qaim. The U.S. military said nearly 50 terrorists were killed during the five-day operation.

During those five days, the Iraqi Security Forces and Marines discovered four hostages bound and gagged in an insurgent torture house, the U.S. military said.

Operation Dagger took place north of Baghdad. It was aimed at uprooting foreign-fighter networks.

The U.S.-led coalition has carried out other offensive and raids in recent months, detaining hundreds of suspected terrorists. Consequently, the U.S. military said Monday it's expanding its overcrowded prisons across Iraq to hold as many as 16,000 detainees.

The prison population at three military complexes throughout the country — Abu Ghraib, Camp Bucca and Camp Cropper — has nearly doubled from 5,435 in June 2004 to 10,002 now, said Lt. Col. Guy Rudisill, a spokesman for detainee operations in Iraq. Some 400 non-Iraqis are among the inmates, according to the military.

All renovations should be done by February.

There have been positive developments in the year since the June 28, 2004, handover, the most notable being the election of the 275-member National Assembly on Jan. 30, Iraq's first free vote in a half-century.

Smaller gains have been made as well.

The number of telephone and Internet subscribers has increased nearly threefold, according to the Washington-based Brookings Institution (search), and the number of trained Iraqi judges has doubled.

However, the terrorist insurgency — estimated at about 16,000 Iraqi militants and foreign fighters — has drastically overshadowed the improvements and created havoc around the country. The situation has forced the implementation of a daily 11 p.m. curfew in Baghdad.

FOX News' Nick Simeone and The Associated Press contributed to this report.