Militants led by the jihadist Islamic State in Iraq and the Levant (Isis) took over parts of the cities of Falluja and Ramadi in late December.
Since then, troops and allied tribesmen have struggled to regain control.
The number displaced by the unrest is the highest since the peak of the sectarian insurgency from 2006 to 2008.
A further 1.1 million internally displaced people (IDPs) have still not returned to communities in Iraq wracked by violence since 2003.
By Nahed  AbouzeidBBC Arabic, Baghdad
The tourist village of Habbaniya, south-west of Falluja, was once a popular destination for the Iraqi elite during Saddam Hussein's rule. It has now turned into a refuge for those fleeing the fighting in Anbar.
Inside the village's chalets and seven-story hotel are hundreds of families, crammed into rooms that lack adequate sanitation and other basic facilities.
In the absence of appropriate medical care due to the army's blockade of the area, skin diseases and viral and bacterial infections are spreading uncontrollably. Children and women are the most vulnerable, especially pregnant women who cannot get access to female doctors.
The main roads in and out of Fallujah and Ramadi are part of the battlefield as the army aims to secure supply routes for troops and tries to cut off militant groups.
The UN High Commissioner for Refugees (UNHCR) said some 50,000 families had fled their homes since clashes erupted in Ramadi and Falluja after security forces dismantled a long-standing anti-government protest camp led by the Sunni Arab community.
While security forces backed by pro-government tribesmen have made steady progress in retaking areas of Ramadi, they have not launched an offensive to recapture Falluja, fearing a repeat of the two bloody urban battles US troops fought in the city in 2004.
Over the weekend, Anbar Governor Ahmed al-Dulaimi gave the militants a week to surrender, but said officials would not negotiate with Isis.
"With the conflict in Anbar continuing UN agencies continue to receive reports of civilian casualties and sustained hardship in communities impacted by the fighting and the influx of internally displaced persons," said UNHCR spokeswoman Melissa Fleming.
Most of the displaced had fled to outlying communities in Anbar province, while 60,000 had ended up in more distant provinces, she added. Many are living in schools, mosques and other public buildings and urgently needed humanitarian aid.
In Anbar, Ms Fleming said access remained a challenge, citing reports that a consignment of World Health Organisation (WHO) medical supplies had been detained at an Iraqi army checkpoint since 30 January.
Many bridges have also been destroyed and roads blocked.
Up to 300,000 people have now been displaced by the fighting between Sunni militants and security forces in Iraq's western province of Anbar, the UN says.