* Amnesty says makes mockery of EU's Nobel Peace Prize
* Economic downturn seen as significant factor
* Greece says handles disproportionate share of immigrants
ATHENS, Dec 20 (Reuters) - Greece is detaining migrants, including children, in inhuman conditions unworthy of a member country of the European Union, human rights group Amnesty International said on Thursday.
Greece - the main entry point into the European Union for Asian and African migrants - has long struggled with illegal immigration, a situation worsened by a deep economic crisis that has boosted anti-immigrant sentiment among Greeks.
In a report, Amnesty said the tens of thousands of migrants who cross into the heavily indebted nation each year struggle to lodge asylum claims, face appalling conditions in detention and racist attacks at the hands of far-right groups.
A new agency set up in 2011 to hear asylum applications is yet to process a single case due to staffing shortages, it said.
"Greece's failure to respect the rights of migrants and asylum-seekers is taking on the proportions of a humanitarian crisis," John Dalhuisen, the group's Europe and Central Asia director said in a statement.
"The current situation in Greece is totally unworthy of the Nobel Peace Prize-winning European Union and so far below international human rights standards as to make a mockery of them."
Greek officials blame the so-called Dublin II treaty - which deems asylum seekers to be the responsibility of the country where they entered Europe - for leaving border states like Greece with an outsized migrant population and say Europe must do more to help the country handle the flow of migrants.
In its critique, Amnesty cited accounts of Syrians fleeing conflict being pushed back to Turkey by Greek authorities, including one alleged incident of a policeman sinking the migrants' inflatable boat by stabbing it with a knife and leaving them to swim back.
Those who make it in to Greece must queue for days in a line that stretches to hundreds of people down the street in Athens for the chance to be one of the 20 allowed to register asylum claims each week, with fights breaking out for a place in line, the group said.
Those who fail to apply for asylum risk arrest in police sweeps and detention in overcrowded, unhygienic facilities for up to a year or more, the group said, citing centres with filthy toilets, no natural light and poor quality drinking water.
"The Greek authorities continue to systematically detain asylum-seekers and irregular migrants including unaccompanied children in breach of international standards and seem to use detention - often in appalling conditions - as a deterrent," said Dalhuisen.
The report cited examples of children separated from their families. It said the youngsters were held in poor conditions among adults and released without access to shelter if no place was found for them at a reception centre.
Migrants were also increasingly at risk from racist attacks, Amnesty said.
"The burden on Greece is great, and given the current economic crisis, increasingly difficult for it to deal with alone," the report said. "However, this cannot excuse the impediments that deny people their rights, the xenophobic rhetoric, or the racist attacks."
For a Reuters report on migrants in Greece, click on:
(Reporting by Deepa Babington; Editing by Michael Roddy)