(This October 14 story corrects to add dropped reference to food in sixth paragraph and clarify distance of trek in tenth paragraph)

GENEVA (Reuters) - Thousands of Ethiopians trekking through desert heat and war in Yemen for the sake of a low-paid job in Saudi Arabia risk getting stuck in an overcrowded migrant camp in Djibouti, the International Organization for Migration (IOM) said on Friday.

Three boatloads have recently been returned from the Yemeni port of Aden, potentially closing a route used by 10,000 migrants per month, mainly Ethiopians from the Oromia and Tigray regions and Somalis.

“If they increase deportations we are going to get people stuck here,” IOM’s regional director Jeffrey Labovitz told reporters in Geneva by phone from Djibouti.

The transit camp at Obock, comprising some tents and corrugated metal sheets and concrete blocks, has swollen from a few hundred people to 600 or 700, and IOM fears another 3,000 deportees could arrive within days.

“If you look at our numbers right now, 600-700 is not huge, but with 10,000 plus per month, if returns start happening, it could very soon get huge,” Labovitz said.

Both sides in a civil war afflicting Yemen have detained thousands of migrants. IOM has been asked to provide food for 4,000 held by Iran-aligned Houthi fighters and estimates several thousand more are held by Yemeni government forces which are backed by a Saudi-led military coalition.

“What’s happening now is a confluence of a whole bunch of political events where suddenly we have a surge in numbers,” Labovitz said.

The situation has been exacerbated by Ethiopia declaring a state of emergency, which temporarily prevented IOM helping Ethiopians willing to return. The situation is further complicated because many of the migrants have no documents and about one in five is a child.

There are almost no women in the camp, and the speculation is that the people smugglers who organize the journey send women, who are in higher demand from Saudi employers, directly by car.

The men and boys - many as young as 11 and traveling unaccompanied - trek 50 km (30 miles) from the Ethiopian border, and as much as 300 km in all, through searing heat and a boulder-strewn desert.

“It’s certainly hundreds who are lost in the desert (each year) and found later by local communities and buried under these omnipresent rocks,” said Labovitz. “It’s not pretty. They dry up and become petrified and are found later by local tribesmen.”

The U.N. refugee agency UNHCR estimates another 70-75 die in the sea crossing to Yemen, but that is likely an underestimate.

“This route doesn’t get the attention it deserves because they are going to Saudi and not going to the shores of the Mediterranean,” Labovitz said.