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Pictures of a toddler's lifeless body washed up on a Turkish beach have sparked horror in Europe as the continent grapples with the biggest humanitarian crisis since the end of World War II.

A Turkish police officer carries the child's body from the beach in Bodrum, southern Turkey. ( AFP: Dogan News Agency )

Key points: Images of drowned toddler identified as Aylan Kurdi on front pages all over Europe

Images of drowned toddler identified as Aylan Kurdi on front pages all over Europe Child believed to be one of 12 Syrians trying to reach Greece before boats sank

Child believed to be one of 12 Syrians trying to reach Greece before boats sank More than 75,000 people in Britain sign petition urging government to accept more asylum seekers

The images of a tiny child lying face down in the surf at one of Turkey's main tourist resorts have been printed on the front pages newspapers all over Europe, putting a human face on the dangers faced by tens of thousands of desperate people who risk life and limb to seek a new life in Europe.

The boy, wearing a red t-shirt and blue shorts, has been identified as three-year-old Aylan Kurdi from Kobani, a war-torn Kurdish town on the Turkey-Syria border.

His five-year-old brother Galip and his mother Rihan, 35, have also been identified as being among the 12 Syrians trying to reach Greece who died when their boats sank.

The family had been reportedly trying to emigrate to Canada.

The father said his children "slipped through his hands" as their boat was taking in water en route to Greece.

"I was holding my wife's hand. But my children slipped through my hands," Abdullah Kurdi told Turkey's Dogan news agency of the sinking that also killed his wife and 5-year old child.

"We tried to cling to the boat, but it was deflating. It was dark and everyone was screaming."

He tried to swim to the shore but when he landed his wife and children were nowhere to be found.

Aylan (L) and Galip Kurdi died when their boat sank off the coast of Turkey. ( Supplied )

"If these extraordinarily powerful images of a dead Syrian child washed up on a beach don't change Europe's attitude to refugees, what will?" Britain's Independent said, in remarks echoed in newspapers across the continent.

Canadian media reported that the child's family had tried in vain to join relatives in Canada — where the government has come under fire for failing to take in more Syrian refugees.

But that was denied by the immigration ministry, and by the boy's aunt Tima Kurdi, the source of the media report, who has since clarified her comments.

"There was no record of an application received for Mr Abdullah Kurdi and his family," said a ministry statement.

It said an application had been received for Abdullah's brother Mohammed, but "was returned as it was incomplete".

The Ottawa Citizen had cited Ms Kurdi, who lives in Vancouver, as saying Aylan's family was the "subject of a 'G5' privately sponsored refugee application" that was rejected by Canada's immigration authorities in June.

"I was trying to sponsor them and I have my friends and my neighbours who helped me with the bank deposits, but we couldn't get them out, and that is why they went in the boat," the newspaper quoted her as saying.

"I was even paying rent for them in Turkey, but it is horrible the way they treat Syrians there."

Ms Kurdi later told a press conference she had not filled out an application for Abdullah and his family.

She said she had sought to gain entry to Canada for the brother Mohammed, who is now in Germany, but could only afford to sponsor her brothers one at a time.

Ms Kurdi emigrated to Canada more than 20 years ago, according to local media.

Top diplomats from France, Italy and Germany have urged a rethink of European rules on asylum to allow for a fairer distribution of migrants throughout the 28-member bloc.

The call came as tensions soared between European states over how to tackle the huge influx of asylum seekers and migrants, as thousands more arrived on the Greek mainland, where more than 160,000 people have already landed this year alone.

Over the past week there has been a dramatic spike in the numbers of migrants — mainly from Syria, Afghanistan, Pakistan and Africa — seeking to leave Turkey by sea for Greece in the hope of finding new lives in the European Union.

The Turkish coastguard said two boats had sunk after setting off from the Bodrum peninsula for the Greek Aegean island of Kos early on Wednesday.

Among the dead were five children and a woman, while 15 others were rescued, the coastguard said.

"Do Something, David" the Huffington Post's UK edition said in a direct appeal to British prime minister David Cameron, who has accepted a lower number of asylum seekers in proportion to its population than most other EU countries.

By the end of Wednesday more than 100,000 people in Britain had signed a petition urging the government to accept more asylum seekers and increase support for refugees.

"There is a global refugee crisis. The UK is not offering proportional asylum in comparison with European counterparts," it read.

"We can't allow refugees who have risked their lives to escape horrendous conflict and violence to be left living in dire, unsafe and inhumane conditions in Europe."

The government is obliged to respond to any petition with over 10,000 signatures, and because it reached 100,000 the issue will be considered for debate in parliament.

A separate change.org petition calling on home secretary Theresa May to give "immediate sanctuary to refugees fleeing war and violence" gained 147,000 signatures in four days.

The Independent newspaper also launched its own campaign, calling for Britain to "accept its fair share of refugees", which gained 13,600 signatures in hours.

Mr Cameron insisted on Wednesday that a solution would not be found "simply by taking more and more refugees".

Sorry, this video has expired Toddler's drowning death sparks anguished new debate on Europe's migrant crisis

European trio call for 'more efficient asylum system

In a joint statement late on Wednesday, Germany, France and Italy urged an overhaul of European laws on asylum in a bid to ensure "a fair distribution" of migrants throughout the bloc.

"The current refugee crisis is putting the European Union and all of its member states to a historic test," it said, calling for a "more efficient asylum system for persons in need".

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The question of how to tackle the soaring numbers of migrants and refugees has caused increasing friction between EU members, with several nations warning it was pushing the continent's vaunted "Schengen" system of borderless travel to breaking point.

Greece appealed for an "immediate" EU response to the crisis and urged the United Nations to become involved as two ships brought some 4,300 people to Athens, most of them refugees from war-torn Syria.

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The government chartered the ships in a bid to relieve pressure on Lesbos, one of several Greek islands inundated by thousands crossing from Turkey in flimsy boats.

Fresh protests also erupted in Hungary, a key transit point for the huge numbers of people trekking from Greece through the Balkans in search of a new life in northern Europe.

On Thursday, hundreds of asylum seekers stormed a train at Budapest's main station after police withdrew, cramming children through open windows in the belief they might travel west to Austria and Germany.

Hungary's main railway operator, however, said there were no direct trains leaving to western Europe.

"In the interests of rail travel security, the company has decided that until further notice, direct train services from Budapest to western Europe will not be in service," Hungarian Railways said in a statement.

Several states have warned the influx is placing the 1995 Schengen system at risk which eliminated passport controls between 22 of the EU's 28 countries, as well as non-EU members Iceland, Liechtenstein, Norway and Switzerland.

On Wednesday, Slovakia's foreign minister Miroslav Lajcak said the Schengen zone had "de facto fallen apart".

There is additional friction over the so-called "Dublin" regulations, under which refugees must file their asylum claim in the first EU country they reach.

Meanwhile, nearly 3,000 migrants were rescued Wednesday off the Libyan coast, the Italian coastguard and Doctors without Borders (MSF) said.

In a posting on Twitter, MSF said it had rescued 1,658 people in a joint operation with the Malta-based humanitarian organisation MOAS, while the Italian coast guard said it and the navy had saved 1,219 people, including 838 who were crammed onto three rickety boards.

AFP/ABC