US and Iraqi troops have set up extra checkpoints in the insurgent stronghold town of Ramadi in an effort to restrict the militants' movements.
US troops are operating fresh checkpoints around Ramadi
The city has become a key centre of the Iraqi insurgency, with much of Ramadi no-go areas for US troops.
Commanders stress there are no plans for a full-scale assault on the city.
In Baghdad, which was rocked by a string of explosions on Saturday, 10 bakery workers were kidnapped at gunpoint from a mainly Shia area.
The bodies of nine other men were found elsewhere in the city, bearing signs of torture, police said.
South of Baghdad, a hunt is continuing for two US soldiers missing since an attack on Friday on their checkpoint. Some witnesses say they were kidnapped by masked militants.
In Ramadi, US commanders described the operation to put a stranglehold on insurgent movements as part of "ongoing" operations, and said no extra troops had been deployed to the area.
"We are focusing on multiple sites used by the insurgents to plan and conduct terrorist attacks and store weapons," Lieutenant Colonel Bryan Salas told Reuters news agency.
"We have also set up additional checkpoints to restrict the flow of insurgents, but citizens will still be able to enter and leave the city."
He added: "This is just one part of a long-term plan to restore stability to Ramadi."
Reports suggested that the US and Iraqi troops had moved into fresh positions to the south of the city.
"The good news is that we didn't get as much resistance as we're prepared for," Lieutenant Colonel V J Tedesco was quoted by AP news agency as saying. "I really think the fight will be in the coming days."
Some 400,000 people live in Ramadi. The city is the capital of Anbar province, which stretches into the desert to the west of Baghdad.
The province has been a centre of resistance since the early days of the insurgency, and many districts of the city are said to be under control of insurgents.
Are you a resident in Ramadi?
We would like to hear from you.
Please send us your stories using the form below.
The BBC may edit your comments and not all emails will be published. Your comments may be published on any BBC media worldwide.
Of course US allied forces must remember that the innocent iraqis mostly suffered the consequences of such offensive. so US must avoid merciless attacks upon every iraqis as it did in falluja. I equally suggested that foreign occupants should now leave iraq and leave us alone. Becouse they failed to restore peace in our nation.
ameen basheer kibiya, central ramadi
First of all Ramadi has nearly 700,000 residents. Second, thousands have had to flee their homes because 2 weeks ago, many are in temporary camps because it is too dangerous for them to go to Baghdad. They left because the USMC and Iraqi troops went to all neighborhoods and announced on loud speakers that the people should leave because the city would be attacked like Falluja. All signs indicate an assault is eminent, they have completely surrounded the city, cut off the water supply since 1 month, and built towers for their snipers. the stranglehold doesnt affect the insurgent, only the innocent people. We have had many relatives and friends killed by US snipers simply for going out of their houses. The insurgents are the 1st to leave, they will simply move to another city then come back later. That is what they did in Falluja.
Dr. Al Duleimi, Ramadi, Iraq