On Sunday, US marine and British Royal Air Force warplanes attacked vehicles and buildings with laser-guided bombs and missiles in and around the town of Karabilah near the Syrian border, on the third day of an operation against resistance activity called Operation Spear, the US military said.
Super Cobra helicopters, British GR-4 Tornados and US F-16s, and 1000 US marines and Iraqi soldiers on the ground were involved in the fight, the military said.
This is one of the rare instances of British involvement in operations in the vast al-Anbar province.
The military said three fighters were killed in a gun battle outside a mosque in Karabilah, after announcing on Saturday that it had killed about 50 rebels since the start of the offensive on Friday.
US soldier killed
Ten Iraqis, including two women, were wounded in the crossfire when fighters entered homes and used families as human shields, the military said in a statement.
"Marines and Iraqi soldiers were unaware of civilians being located in the homes," the military said.
A thousand US and Iraqi troops
took part in the latest operation
There was no independent confirmation of casualties in the remote region, which is hard for journalists to reach.
The military said soldiers found a bomb factory in Karabilah with devices used to make the roadside bombs and car bombs.
The US military also announced that a marine died on Saturday during Operation Spear - the first American death reported in the twin offensives.
The military said the marine, assigned to Regimental Combat Team 2 of the 2nd Marine Division, was killed by small-arms fire during Operation Spear.
At least 1722 members of the US military have died since the the March 2003 Invasion.
The US's latest operations followed similar sweeps this year in the same Euphrates valley area, including one in early May.
In a further effort to restrict the movement of fighters operating in Anbar, another US-Iraqi force of about 1000 men is concentrated on an area around Lake Tharthar, northwest of Baghdad, as part of Operation Khanjar, Arabic for dagger.
The lake separates Anbar from Salaheddin province, another predominantly Sunni Arab province, where resistance is active.
Al-Jaafari (L) was in Kuwait to
discuss buying oil
"Operation Khanjar is focused on locating hidden weapons caches and denying insurgents sanctuary in the area that is a suspected insurgent and terrorist logistical hub," the US military said.
In late March, Iraqi and US officials said they killed 85 fighters in an air strike on a lakeside training camp for former government and al-Qaida fighters. Rebels told an AFP correspondent only 11 were killed.
Al-Jaafari in Kuwait
Meanwhile, Iraqi Prime Minister Ibrahim al-Jaafari was in Kuwait with Oil Minister Ibrahim Bahr al-Ulum to discuss buying more Kuwaiti fuel and selling natural gas to its southern neighbour.
In Ankara, the kidnappers of a Turkish businessman taken hostage last month in Iraq have demanded a ransom of several million dollars to free the man, his family said on Saturday.
Ali Musluoglu, 48, was abducted on 19 May and in a 7 June video, kidnappers threatened to kill him in four days if Turkey did not end all support for US forces and businesses in Iraq.