IS overran large areas of both countries in 2014, declaring a "caliphate" in territory it controlled, but the jihadist group has since lost ground to Iraqi forces and faced advances from different groups in Syria.
Amid intense fighting in recent days, the thousands of displaced have been seen arriving in areas outside IS control, many hungry and terrified after years under jihadist rule.
In Iraq, the offensive by US-backed Iraqi forces to retake west Mosul from IS has displaced more than 45,000 people in little more than a week, the UN migration agency said.
In neighbouring Syria, more than 26,000 people have been forced to flee fighting in the country's north in the same period from February 25, UN humanitarian agency OCHA said.
Before the battle for Mosul was launched in October, a million-plus civilians were thought to still live inside Iraq's second city, which is IS's last major bastion in the country.
Iraqi forces backed by US air strikes in January retook the eastern side of the city, which is divided by the river Tigris, before setting their sights on its smaller but more densely populated west.
They launched a major push to recapture west Mosul from IS on February 19, retaking the airport and then pushing up into the city from the south.
Families escaping the battle for west Mosul have arrived in droves at sites for the displaced in the past week, the International Organization for Migration said.
- 'Left with nothing' -
On Saturday, Iraq's minister of displacement and migration criticised UN-led efforts to aid those displaced by the fighting, while the UN said that such assistance is the "top priority".
More than 200,000 are currently displaced as a result of the Mosul operation, while more fled but later returned to their homes, according to the IOM.
In Syria, OCHA said 26,000 people had fled areas where government forces backed by Russian air power have been waging a fierce offensive against IS.
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Those areas lie east of the town of Al-Bab, which Turkey-backed rebels seized from IS on February 23 after several months of fighting in another advance on the jihadist group.
The UN agency said the nearly 40,000 people displaced from the town since November fled north to areas controlled by other rebel forces.
Many have sought refuge in areas around Manbij, a town controlled by the US-backed Syrian Democratic Forces.
An AFP correspondent in Manbij said that long queues of families were still forming at checkpoints leading to the town on Sunday.
Pick-up trucks full of children and women wearing full black veils were being searched by SDF personnel before being allowed to enter.
The Syrian Observatory for Human Rights monitoring group said Saturday that 30,000 people had been displaced by the government's offensive on IS.
The push is aimed at IS-held Khafsah, the main station pumping water into Aleppo.
Residents of Syria's second city, under full regime control since December, have been without mains water for 48 days after the jihadists cut the supply.
On Sunday, Russian and regime warplanes bombarded IS positions in support of Syrian troops, which had advanced to around 11 kilometres (nine miles) from Khafsah, the Observatory said.
Since war broke out in Syria in March 2011, more than half of its pre-war population has been forced to flee their homes.
Aleppo province hosts tens of thousands of displaced Syrians, many in camps near the Turkish border.
"We left our homes with nothing: no fuel, no bread. Our children are starving," said Jumana, a 25-year old Syrian woman who fled the clashes with her two children.
Turkey launched an unprecedented military campaign inside Syria in August, backing opposition rebels to fight IS. But it views the Syrian Kurds who lead the SDF as "terrorists".
The SDF are pressing an advance towards retaking the group's de-facto capital of Raqa, backed by a US-led coalition that has been carrying out air strikes in Syria and Iraq since 2014.