Forty would-be immigrants died when their boat sank in the Aegean Sea
Greece has rejected strong criticism of its handling of asylum seekers by the UN High Commissioner for Refugees.
The UN body said the most vulnerable people were often unable to claim asylum and others were not guaranteed a fair evaluation of their claims.
Finland responded by saying it would stop sending migrants back to Greece unless it could promise fair treatment.
But Greece says the UN's accusations are untrue and it is trying to be fair in handling a big surge in migration.
The Hellenic Police Head of Asylum, Nikolas Stavrakakis, told the BBC News website: "In 2006 we had approximately 12,500 applicants, and the next year they more than doubled".
ASYLUM CLAIMS IN EUROPE
Greece 25,113: 0.04% granted refugee status + 2.05% on appeal
UK 27,905: 34% granted refugee status + 24% on appeal
Sweden 36,370: 56% granted refugee status + 14% on appeal
Germany 19,164: 20% granted refugee status + 94% of the remainder on appeal
Source UNHCR 2007
The UNHCR report last week said that of 25,113 asylum claims registered in Greece in 2007, eight were granted refugee status at the start of the process and another 138 were added on appeal.
The report also draws attention to a large backlog of asylum claims with the waiting period lasting up to four years.
"We are all over the country trying to screen the real people from those coming for economic reasons," says Mr Stavrakakis.
"We have big pressure and you have to be careful in order to be fair in this process. That's why we have a lot of delays. All these accusations are untrue."
Many of the migrants who come to Greece arrive via Turkey in an attempt to claim asylum in the European Union.
Earlier this month, 190 illegal immigrants were detained in a series of operations in Turkey. Fifty-six of them were picked up on the Aegean coast at Seferihisar.
It is a short boat trip from the Turkish mainland to the Greek islands of Chios and Samos and, last December, at least 40 people died when their overcrowded boat capsized off the Turkish coast.
For those who do make it, their asylum claims should be handled in Greece, according to EU rules.
Under the "Dublin II" regulation, asylum seekers generally have to be processed by the first EU member state they come to.
Many of those who arrive in Greece move elsewhere, but are sent back as they have not been processed. Finland said it would halt the return of refugees to Greece until it had written guarantees that their asylum applications were dealt with.
Speaking after an EU home affairs meeting last week, Greek Interior Minister Prokopis Pavlopoulos said his country would fall in line with EU regulations before the end of June.
He said he had received very strong support from EU ministers and assured reporters about the treatment of migrants in Greece.
"Our first and only concern is respect for the human rights of all who arrive in Greece."