Greece and Turkey, countries that are the main routes for illegal migrants and refugees entering Europe, have rejected threats from the European Union (EU) that they would be saddled with most of these refugees unless they strengthened their border controls.

Mr Alexis Tsipras, the Greek Prime Minister, has complained that an EU plan to create more refugee-processing camps in his country risks making Greece a "black box" for all migration.

And Mr Selim Yenel, Turkey's Ambassador to the EU, has dismissed European demands that his country close the sea routes illegal immigrants take to Europe as "unacceptable" and "not feasible".

"Forget it," Mr Yenel bluntly told EU governments.

Still, an EU summit scheduled for next week will examine measures aimed at forcing Greece and Turkey to seal their borders to newcomers.

"The flow of migrants arriving in Greece from Turkey is too high," stated a draft version of the summit communique.

Greek Coast Guard officers transferring a baby to the safety of their vessel from a dinghy carrying refugees and migrants during a rescue operation in the open sea between the Turkish coast and the Greek island of Lesbos on Monday. PHOTO: REUTERS

Under existing European migration rules, asylum seekers must stay in the first EU member-state they entered, and the government of that state is responsible for their welfare.

This includes an obligation to take them back, should the refugees cross the border into another EU member country.

But these arrangements collapsed last August, when German Chancellor Angela Merkel announced that her country would accept refugees regardless of where they came from. That made Germany a magnet for asylum seekers from neighbouring states. It also gave Greece, where most migrants from the Middle East arrive, an incentive to avoid documenting them altogether.

On Wednesday, the European Commission, the EU's executive body, gave Greece one month to stop this "pass-the-parcel" strategy. Mr Dimitris Avramopoulos, the European Commissioner in charge of migration policy and a Greek himself, has told his native state that it must resume documenting all incoming migrants, process their asylum applications speedily, and improve terrible living conditions for refugees in Greece which were once condemned by the European Court of Human Rights as tantamount to "degrading treatment".

Mr Avramopoulos has acknowledged that Greece, which has tottered on the brink of bankruptcy for years and where a quarter of the population is unemployed, "must not be put under more burden".

Instead, he plans to create five EU-funded "migration hot spots", effectively new camps where refugees can be documented. One such hot spot is already in operation and, the EU claims, has boosted the fingerprinting of migrants from 8 per cent of new arrivals in Greece last year to around 78 per cent today.

However, the problem for the Greek government is not only the burden involved, but also the realisation that once fingerprinted, migrants could be returned to Greece should Germany close its borders, as the Germans are almost bound to do in the near future. That could saddle the Greeks with hundreds of thousands of migrants, and probably for years if not decades.

Largely in order to alleviate Greek fears, EU officials are also offering neighbouring Turkey a new deal intended to incentivise the country to close its borders. Under a plan touted by the Netherlands, which currently has the presidency of the EU, Europe will promise to take 250,000 refugees each year directly from Turkey, provided the Turks undertake to police their sea routes and prevent asylum seekers from crossing into Europe. Dr Merkel also pushed the scheme during a visit to Turkey earlier in the week.

But there are scant chances of Turkey accepting such an arrangement.

The Turks, who have already admitted 2.5 million refugees from Syria, find it offensive to get lectures from Europe on how they should absorb even more.

Turkey also knows that, even if Europe keeps its pledge and admits 250,000 refugees each year, that would only increase the number of refugees piling up on Turkish soil.

The International Organisation for Migration estimated that around 1.2 million people will flee Syria this year alone, largely because of the current military offensive of the Syrian army, assisted by Russia.

What Turkey wants is not help with refugees, but European assistance in putting an end to the war in Syria.

"I find it hypocritical that some circles are telling Turkey to 'open your borders' while, at the same time, failing to tell Russia 'enough is enough'," said Turkish Prime Minister Ahmet Davutoglu during a visit to the Netherlands this week.

Undaunted, EU heads of government plan to discuss again the proposals for Greece and Turkey at the special summit in Brussels next week.

But progress will be slow and the sense of political paralysis in Europe remains evident.