BAGHDAD, Iraq - They want to be invisible, these young women at Baghdad University explained. They were sitting in a small group - five students with pale head scarves pulled tightly around their somber faces.

They would not give their names. That would be crazy, they said. The whole point of wearing the scarves now was to be anonymous and unimportant, to avoid being singled out and followed, or kidnapped, or shot. It was more than a matter of blending in. It was a matter of disappearing into the landscape.

"I put on the scarf because I wanted to walk in the street without fearing someone will kill me or kidnap me," said one of the women. "I want to finish my studies. Without the scarf I cannot. I heard rumors about killing women without a scarf. Why should I risk my life?"

This is the new reality for many women in Iraq, Muslims and Christians alike. As the months have passed since the U.S.-led attack, fewer women are daring to venture out without wearing a traditional Muslim head scarf, called a hejab in Arabic. In Baghdad, moderate Muslim women used to feel they had a choice whether to wear the scarf. Now, in many neighborhoods, it is hard to find a woman outdoors without one.

Conservative Muslims believe that women should cover their heads to hide their beauty and not tempt the men who see them. Such instructions are spelled out in the Koran, the Islamic holy book.

The practice of wearing head scarves varies widely throughout the Islamic world, from more secular countries like Turkey where many women dress in the Western style, to strict religious societies like Saudi Arabia where all women cover their heads and most of their faces in public.

In the past several years, an increasing number of Muslim women living in Western Europe have begun wearing scarves - in some cases as a religious statement, in other cases because of pressure from other local immigrants.

Although Iraq is predominantly Muslim, for many decades its capital was a trendy, modern city. In the 1960s, women wore short skirts and blouses with low necklines. But their daughters say they do not have such freedom today. They blame a post-war insurgency bolstered by conservative hard-liners.

"Because of the current situation in the country, lack of security, the occupation and many other things, people started to look for a way to escape the terror," said Fadhil Shaker, a psychology professor at Baghdad University. "They want to hide or take shelter to protect themselves. For women, the scarf is the best way to protect them. Women believe the scarf will be the wall to prevent people from looking at them."

Before the war, Iraqi Christian women rarely put on scarves. There was no reason to do so, according to Christian women interviewed recently. Their religion did not dictate it, Muslims and Christians in Iraq got along peacefully and they said they felt no pressure to blend in. Even a few months ago, the sight of a Christian woman without a scarf or a Catholic nun in a habit was not uncommon in neighborhoods where Christians gathered.

But these days Iraqi society feels like it has lost its social compact, its religious tolerance, many of the women said. Christians feel singled out. Anyone associated with the Americans, any foreign military force or the interim government feels singled out.

Nada, a student who declined to give her last name, said the first day she went to college this fall, her mother rushed out of the house at the last moment and presented her with a scarf. She had never worn one.

Female students at Baghdad University now debate whether women should wear the scarves. Some, wear them for religious reasons. But most who have recently adopted the practice have done so simply out of fear.

"If a woman or a girl is in scarf, she could save herself many problems," said a Muslim student who spoke on condition of anonymity. "I come to the university comfortable because I know men won't look at a woman in scarf, or at least they will not bother me. The scarf helps me to walk in the street freely."

The student said she believed Muslim women should wear scarves, though she said she did not feel pressured to wear one.

"That's what our religion demands," she said. "But that doesn't mean we force people to put it on. People should understand why they have to put on hejab first; otherwise there is no point of it on the head."

Noor Ali, 19, said she has chosen to wear a scarf since she was 14, but she also cannot stand the idea that women would feel forced to put on the full cloth headdress - one piece that crosses the forehead to hide the hairline completely, the other a longer drape that covers the head.

"Those who want to force women to put on a scarf want nothing (Western) to spread in Iraq," she said. "They want us to be another Kabul," she added, referring to the capital of Afghanistan, which was ruled from 1996 to 2001 by the Taliban, an Islamic extremist militia.

"The Taliban failed there, and they want to try in Iraq," Ali said. "Everyone should be free to choose whether to put the scarf on or not. It is not us who judge. There is a God, and he will eventually decide this."

Dalal Jabbar, 19, a resident of Sadr City, a poor Shiite Muslim neighborhood in Baghdad, said Iraqi women are more afraid today than ever before.

"There is no law to rule the country," she said. "I see the scarves as the best way to protect ourselves in Iraq now. When I walk in the street, I know I'll have no trouble, because men prefer to look at others without a scarf, more than me."

A woman who gave her name as Dalia, 21, an engineering student at Baghdad University, agreed that forcing women to wear scarves was not the way to win people over.

"We cannot force people to believe in what we believe in," said Dalia, who is Muslim. "They even want the Christians to put on a scarf. Christians have their religion and convictions, which differ from ours. We cannot force them to do what we want. We want to have our country secured and stable, and I think forcing people to do what they don't want will add nothing but tension."

Dalia said she is one of the few women at her university who does not wear a scarf.

"The scarf has nothing to do with faith," she said. "I fear there will be time when we cannot walk in the street without head-to-toe abaya (the full black traditional dress) and a face cover. This will be the end of Iraq as a civilized country."