(Adds quote, UNICEF comment)

GENEVA, Aug 7 (Reuters) - Some of the many thousands of people trapped by Islamic State militants on Sinjar mountain in northern Iraq have been rescued in the past 24 hours, a spokesman for the U.N. Office for the Coordination of Humanitarian Affairs said on Thursday.

The militants' capture of the nearby town of Sinjar, ancestral home of the Yazidi ethnic minority, had prompted tens of thousands of people to flee to the surrounding mountains.

"We're just receiving the information right now. We've just heard that people over the last 24 hours have been extracted and the U.N. is mobilizing resources to ensure that these people are assisted on arrival," David Swanson said by phone from Iraq.

"This is a tragedy of immense proportions, impacting the lives of hundreds of thousands of people," he said.

"Over the past couple of days, almost 200,000 people have made their way northwards to Iraq's Kurdistan region, Dohuk governorate, or to disputed border areas inside Ninewah," he said.

"We have also received reports that thousands more may have fled across the border into Syria, and are waiting to cross back into Iraq, but I have no concrete confirmation of that."

Sinjar district previously had a population of 308,000.

"Many of the displaced are in immediate need of essential life-saving humanitarian items, including water, food, shelter and medicine."

He did not have details of the number of people who might have been evacuated or who was extracting them.

A spokesman for the U.N. children's agency UNICEF in Geneva, Christopher Tidey, said most of the families remained on the mountain.

"We have received reports of dehydrated children and we know that at least 40 children have died," Tidey said.

The militants extended their gains in northern Iraq on Thursday, seizing more towns and strengthening a foothold near the Kurdish region, witnesses said, in an offensive that has alarmed the Baghdad government and regional powers. (Reporting by Tom Miles; Editing by Toby Chopra)