Al-Maliki and Rashid vowed to work together to combat al-Qaeda insurgents who have been fighting in Anbar since the US-led invasion began in March 2003.
During the prime minister's visit, Iraqi and US troops patrolled Ramadi's streets in large numbers and a vehicle curfew was imposed.
US commanders said they saw al-Maliki's trip as a concrete sign that his Shia-led government is serious about working with Anbar's Sunni leaders, many of whom have turned against the insurgency.
|"It's very exciting to have the prime minister in Anbar. It shows that nothing's impossible"|
John Allen, US Brigadier General
"It's very exciting to have the prime minister in Anbar," said John Allen, US Brigadier General. "It shows that nothing's impossible."
Al-Maliki's party held a day of meetings with Anbar leaders and tribal sheikhs, including some of those now fighting al-Qaeda insurgents in the province.
Many ordinary Sunnis distrust or oppose Maliki's Shia-led government, feeding support for a wider Sunni insurgency across Iraq.
More US troops
surfdog1958, Baton Rouge, USA
Send us your viewsThe new US commander in Iraq, General David Petraeus, was also in Ramadi on Tuesday, touring US and Iraqi units.
The coalition says Al-Qaeda fighters have taken deep root in Anbar, which stretches west from Baghdad to the borders with Saudi Arabia, Jordan and Syria.
The US military and the Iraqi government have as yet failed to assert their will among the fiercely-independent Sunni tribes living in the province.
Additional US troops are deploying in Baghdad and Anbar in support of a new security plan which has already seen the deployment of about 90,000 Iraqi and US soldiers in Baghdad.