Restrictions on Iraqi people fleeing the fighting in Anbar province are forcing some of them to return straight into conflict areas, an aid group said Tuesday.

"Thousands of people fleeing Ramadi are stuck at checkpoints or being denied entry to safe areas," said Mark Schnellbaecher of the International Rescue Committee (IRC).

"For some people the situation has become so hopeless that they are returning to the conflict in Ramadi," he said in a statement.

Thousands of people who fled the Islamic State group's takeover of Ramadi this month have been stuck at Bzeibez bridge for days, barred from leaving Anbar.

The IRC said the checks conducted on displaced families were done so inconsistently, with in some places a blanket ban on men and in others not.

"Security checks should never be arbitrary or discriminatory, and every effort should be made to keep families together," Schnellbaecher said.

The floating bridge at Bzeibez, which connects Anbar to Baghdad or other areas where displaced people have sought shelter further south such as Hilla and Najaf, was open Tuesday.

But it has been largely closed during the past two weeks, with families asked to produce a sponsorship before crossing, a measure meant to combat fears that groups of displaced from Anbar could be infiltrated by IS.

"The sponsorship system is leading to serious exploitation, with some sponsors selling their sponsorship for up to $700," the IRC said.

The group argued that the phenomenon put "unacceptable financial burden on an already extremely vulnerable population" and undermined the security rationale of the measure.

According to the United Nations, at least 55,000 people have fled the fighting in Ramadi, which fell to IS on May 17 after a chaotic retreat by the Iraqi security forces.

Of the 2.8 million people who were displaced by violence in Iraq since the start of 2014, around 900,000 of them are from Anbar.

The vast western province is where government and allied forces are now focusing their efforts, with thousands of regular forces and paramilitary fighters converging on Ramadi to wrest it back from the jihadists.