The exodus is the latest in the aftermath of the fall of the city of Ramadi, the capital of Anbar, Iraq's largest Sunni province to the Islamic State over the weekend.
The Shiite-led government in Baghdad is struggling to come up with a plan to reverse the stunning loss of the city, pledging a counter-offensive and relying on Iranian-backed Shiite militiamen to join the offensive.
Athal al-Fahdawi, an Anbar councilman, said that thousands of civilians from Ramadi who were stranded on open land for days, are now being allowed to cross a bridge spanning the Euphrates River and enter Baghdad province.
According to the International Organisation for Migration, more than 40,000 people have been displaced from Anbar province since Friday, when IS conquered Ramadi.
In the past, people fleeing Anbar have been prevented from entering Baghdad due to fear that militants might mingle in with the crowds and sneak into the Iraqi capital.
Meanwhile, residents still left in Ramadi told The Associated Press over the phone today that Islamic State militants were urging them over loudspeakers not to be afraid and to stay in the city, already suffering from acute shortages of food and medicines.
It is still unknown when the expected wide-scale operation to recapture Ramadi and other cities will start.
Baghdad officials and leaders of the so-called Popular Mobilisation Units, which consists of a number of Shiite militias who are fighting on the side of the Iraqi military and security forces, have repeatedly said they need time for a military buildup and reconnaissance.
When the Islamic State launched its blitz last year and entire cities and towns fell into the hands of the militants, the Iraqi government at first took only defensive measures and in many cases, soldiers and Iraqi forces abandoned their posts and fled in the face of the IS assault.
