They met unexpected resistance from insurgents hidden in remote desert outposts along the waterway’s southern shores, however.
Marines fought house-to-house against dozens of well-armed insurgents firing at them from balconies, rooftops and sandbagged bunkers in the border town of Obeidi and surrounding villages.
As many as 100 militants have been killed since Operation Matador, one of the largest American offensives in Iraq in six months, began on Saturday night in Qaim, 322 kilometres west of Baghdad, the military said.
At least three US marines have been killed in the offensive, which involves more than 1,000 marines, sailors and soldiers backed by helicopter gunships and fighter jets.
Gunmen have kidnapped the governor of the western Anbar province and told his family he would be released when US forces withdraw from Qaim.
Raja Nawaf Farhan al-Mahalawi was seized as he drove from Qaim to the provincial capital of Ramadi yesterday morning, his brother Hammad said.
The kidnappers phoned the family and said they were holding the governor until the US pulled out of the Syrian border town.
Meanwhile, two US allies in Iraq were grappling with hostage crises after Japan confirmed one of its citizens was missing and a deadline set by the captors of an Australian passed with no word on his fate.
One of Iraq’s most feared insurgent groups, the Army of Ansar al-Sunna, said in an internet statement it had ambushed a foreign security convoy near a US base in western Iraq and captured a Japanese citizen. A picture of the man’s passport posted on the internet gave his name as Akihiko Saito, aged 44.
Ansar al-Sunna has killed scores of hostages, including foreigners from countries with no connection to the Iraq war. Last August the group killed 12 Nepalese migrant workers, beheading one and then riddling the others with bullets.
Another insurgent group, the Shura Council of the Mujahideen in Iraq, is holding an Australian hostage - 63-year-old engineer Douglas Wood, seized in Baghdad last month.
The latest US offensive comes amid a surge of militant attacks across Iraq, often targeting security forces and civilians, since the new government was announced on April 28.
At least two car bombs exploded in central Baghdad yesterday, killing at least seven people and wounding 19. Three American soldiers were among the injured.
US Marine Capt Jeffrey Pool said soldiers built a pontoon bridge across the Euphrates River and marines had pushed into the northern Jazirah Desert, a largely unpatrolled area near the Syrian border.
“This is an area which we believe has been pretty heavy with foreign insurgents from many different areas - Syria, Jordan, Saudi Arabia, Palestine,” Lt Col Steven Boylan, a spokesperson for US forces in Iraq said. “That’s a fairly porous area of the border because of the terrain. It is very difficult.”
Residents in the area reported fighting yesterday in Obeidi, 298 kilometres west of Baghdad, and the two nearby towns of Rommana and Karabilah. They said frightened residents were fleeing the Qaim area.
“It’s truly horrific, there are snipers everywhere, rockets, no food, no electricity,” Abu Omar al-Ani, a father of three, said from Qaim. “Today five rockets fell in front of my house... we are mentally exhausted.”
Capt Pool said insurgents tried to launch a counter-attack on Monday night seven kilometres from US Camp Gannon in Qaim.