Some radical clerics demand that all women wear the veil
UN officials in Baghdad say they are very concerned that religious extremists are intimidating women and girls into wearing the veil.
In particular, some radical clerics have demanded that women - even Christians - wear the veil.
The UN officials have also expressed alarm at a reported rise in rape.
Since the end of the conflict in Iraq, radical factions in Iraq's Sunni and Shia Muslim communities have been asserting themselves in the ensuing period of instability.
One Iraqi UN staff member recently received a handwritten letter at home saying she would be killed unless she started covering her hair.
The spokesman for the UN Children's Fund, Geoffrey Keele, said that in some areas there had also been pressure on schoolgirls to start putting on the veil.
"It's an issue of people's rights - it's an issue not only of women's rights, but human rights - and people have a right to choose whether or not they wear the veil, what religion they practise, how they practise that religion," he told the BBC.
UN officials have raised the issue with American and British forces.
They also say Iraqi women can no longer drive or walk in the streets at night as freely as they did in pre-war Iraq.
And women have been victims not only of intimidation, but also of the lawlessness of the last few weeks, says the BBC's Caroline Hawley.
No statistics are available, but Iraqis say there has been a significant increase in rape.