towns were starting to reach displacement camps away from the fighting, as Iraqi forces press on with an offensive to retake Islamic State's last major stronghold in Iraq.
The battle that started on Oct. 17 with air and ground support from a U.S.-led coalition is shaping up as the largest in Iraq since the U.S.-led invasion of 2003.
On Tuesday Iraqi forces battled Islamic State fighters on the eastern edge of Mosul as the campaign entered a new phase of urban warfare.
The United Nations has said the Mosul offensive could trigger a humanitarian crisis and a possible refugee exodus if the civilians inside in Mosul seek to escape, with up to one million people fleeing in a worst-case scenario.
"People are starting to arrive now from the small towns around Mosul," Joe Cropp of the International Federation of Red Cross and Red Crescent Societies (IFRC), told the Thomson Reuters Foundation.
"We've been aware that this has been coming up and the preparations have been going on for two months," he said in a phone interview from northern Iraq.
IFRC said many people were arriving with only the clothes they were wearing and those who reached Khazer camp, east of Mosul, said they had to walk through the night.
"We were so worried the children would cry out during the night and we would be discovered," IFRC quoted one of the mothers as saying.
Thousands more people are expected to arrive in the coming days and weeks as fighting around Mosul intensifies, IFRC said. Throughout the country, some 10 million Iraqis are in need of aid.
"Local communities across the country are sharing the responsibility, taking in millions of displaced people. But even with the greatest will in the world they cannot accommodate a million more," Gyula Kadar, IFRC operations manager, said in a statement.
The International Organization for Migration said nearly 21,000 people have been displaced since the start of the campaign, excluding thousands of villagers taken into Mosul by retreating jihadists who used them as human shields.
The U.N. said in October a total of six camps had been built that can accommodate 50,000 people. Efforts were underway to construct 11 more.
Claire Mason, humanitarian policy and advocacy adviser at Save the Children said for security reasons the charity was unable to get too close to Mosul and was readying mobile child protection teams to assist people scattered outside the city.
Betsy Baldwin, Iraq response director from the charity Tearfund, said several hundred people arrived the previous night in one of the camps where the charity was helping.
Baldwin said her organization had been on standby since summer, preparing tents, stoves and winter clothes which it was planning to distribute this week.
"We are just hoping that we can safely access people in need, that the civilians can move safely out of the conflict zones," she told the Thomson Reuters Foundation from Iraq.
International Rescue Committee said in a statement on Wednesday it had heard of people inside Mosul buying cloth to use as white flags when the army arrives.