An Iraqi family's dream of reaching Europe ended in darkness, terror and loss when two of their children drowned in the same boat accident that killed Syrian toddler Aylan Kurdi.

Eight-year-old boy Haidar and 12-year-old girl Zainab were trapped under their small boat when it capsized in the Aegean Sea at night on the way to Greece, a perilous trip being made by a flood of refugees fleeing wars and privation.

Three-year-old Aylan's body was photographed lying in the sand in Bodrum, Turkey after he drowned in the same accident, an image that helped to focus international attention on the plight of refugees.

Zainab Abbas, her husband and their three children left Iraq, travelled to Istanbul and then made their way to Bodrum, on the coast, trying for almost two weeks to make the boat trip to Greece.

There are many reasons for Iraqis to flee their country: much of its west is held by jihadists who carry out frequent bombings in other areas, corruption is rampant and services abysmal.

Though the government has announced reforms, there are major challenges to any real and lasting change, and many Iraqis have lost hope that they, or their children, have a future in the country.

- 'A better life' -

Many Iraqis are making the trip, with more than 9,000 arriving in Greece between January and August this year, the fifth-largest group by nationality, according to the International Organization for Migration (IOM).

"Everyone was talking about this route, so we decided that we would leave, to provide them with a better life," Abbas told journalists near the Baghdad airport.

But travelling to Europe by sea carries deadly risks: more than 2,700 people have died in the Mediterranean this year, including 315 from the Middle East and North Africa, the IOM said.

Abbas and her family finally received the go ahead to make the journey late one night and were driven to the shore to depart.

Smugglers rushed them into a small boat without enough life jackets for everyone -- a boat that also carried Aylan and his family, who were fleeing the civil war in Syria.

Disaster struck almost immediately.

Within six minutes of their departure, the boat shook and the engine stopped, and by the time they restarted it, the boat had begun to leak, Abbas said.

The boat then sped toward a wave and struck it, throwing passengers into the water, then capsized, trapping two of Abbas's children underneath.

- Shouting for lost children -

Abbas, floundering in the dark in the choppy water, was able to touch her daughter's hand, but could not save her.

"I shouted my children's names but they did not respond," she said.

Abbas, her husband and their third child survived the wreck, as did Aylan's father Abdullah, who told AFP by telephone that there was an Iraqi family of five on the boat with him and that they lost two children.

The accident also claimed the lives of Aylan, his four-year-old brother, and his mother.

Abdullah returned home to Syria and buried his wife and two children on Friday.

The bodies of Abbas's two children arrived in Baghdad on Wednesday in plastic-wrapped coffins and were loaded into a the back of a pick-up truck.

They were taken to the Shiite shrine city of Karbala, south of Baghdad, and buried in small graves in the dusty soil as weeping relatives looked on.

Abbas wept over the coffins after they arrived in Baghdad, blaming herself for her children's deaths.

"It's my fault," she said through her tears. "I hoped for a dignified and happy life for you."