(CNN) -- Europe's leaders "should hang their heads in shame" over their failure to take in more than a tiny proportion of refugees who have fled Syria's desperate civil war, rights group Amnesty International said Friday.
European Union nations have offered to open their doors to a little more than 12,000 of the most vulnerable refugees from Syria, Amnesty International said, describing the number as "pitifully low."
The figure represents 0.5% of the more than 2.3 million people who have fled the country since the conflict began in March 2011, according to the rights group's briefing, "An International Failure: The Syrian Refugee Crisis."
More than half the 2.3 million refugees registered by the United Nations are children.
At least 4.25 million have been forced from their homes within Syria, Amnesty International said, making the total number displaced above 6.5 million -- nearly a third of the country's population.
In this dire situation, the countries neighboring Syria -- Lebanon, Jordan, Turkey, Iraq and Egypt -- have taken in 97% of the refugees, according to U.N. figures.
Meanwhile, the EU "has miserably failed to play its part in providing a safe haven to the refugees who have lost all but their lives," said Salil Shetty, secretary-general of Amnesty International. "The number of those it's prepared to resettle is truly pitiful. Across the board European leaders should hang their heads in shame."
Within Europe, 10 EU member nations have promised to resettle 12,340 refugees. Of these, 10,000 places have been offered by Germany. France has pledged 500 places, while Spain has offered 30.
The other 18 EU states -- Britain and Italy among them -- have not made any resettlement pledges, Amnesty International said. Four non-EU European nations have taken in some refugees.
Outside Europe, Australia and Canada have promised to take in about 1,800 refugees between them. The United States has an open-ended number of places as part of its annual resettlement program.
'Perilous journeys by boat or land'
As winter closes in, the situation of refugees packed into temporary camps will only worsen.
A huge storm that dropped snow and rain whipped by high winds onto Turkey, Syria, Jordan and Lebanon this week has added to the suffering. The Bekaa Valley in eastern Lebanon, where thousands of Syrian refugees are living in tents, has been badly affected.
With so few resettlement places offered to Syrian refugees in Europe, many attempt the journey under their own steam, Amnesty International said.
People make risky journeys by sea or other means as they seek illegally to cross Europe's borders, the rights group said. Syrians are among the hundreds to have drowned off the Italian island of Lampedusa this year as they sought to land on EU soil and claim asylum.
Other Syrian refugees who make their way to two major gateways to the EU -- Greece and Bulgaria -- are being "met with deplorable treatment," the report said.
"Tens of thousands are risking perilous journeys by boat or land to try and reach Europe," Shetty said. "We have seen hundreds lose their lives in the Mediterranean. It is deplorable that many of those who have risked life and limb to get here, are either forced back or detained in truly squalid conditions with insufficient food, water or medical care."
Amnesty International points out the EU has provided far more money for border control than for the support of refugees in Greece this year.
Only 55,000 Syrian refugees have managed to gain entry to the EU and claim asylum, the report said.
'Urgent increase' needed
In light of its report, Amnesty International has called for "an urgent and significant increase" in the number of resettlement places offered to refugees from Syria.
It has also urged EU countries to ensure safe passage to Syrians seeking asylum, to treat those rescued in the Mediterranean with respect and to continue to support those countries taking in the huge majority of refugees.
The UK government defended its response to the refugee crisis Friday, saying that while it has "no plans to resettle or provide temporary protection to Syrians," it is providing financial support.
"We are giving as much help as possible to people in the region. We are one of the highest international donors to the Syrian relief effort -- our £500 million (about $813 million) pledged so far is more than the other EU member states combined," a UK government spokesman said.
The United Nations estimates that more than 100,000 people overall have died since the Syrian conflict began in March 2011. Hundreds of thousands of civilians have also been injured.
The conflict began with a government crackdown on peaceful protesters during the Arab Spring movement, then slowly spiraled into a bloody, full-blown civil war.
CNN's Zahra Ullah contributed to this report.