Greek Prime Minister Alexis Tsipras on Friday said a huge influx of migrants and refugees "surpassed" his debt-hit country's abilities as he announced a raft of measures and asked for EU help to handle the crisis.

"This problem surpasses us. Greece is a country in economic crisis, and it faces a major humanitarian crisis within a crisis," Tsipras said.

"These dimensions exceed our country's capabilities, they are European dimensions."

The premier announced a raft of measures to improve government coordination after the UN refugee agency termed Athens' response to the problem "totally shameful".

The UN refugee agency's division for Europe said Greece had provided virtually no reception facilities for 124,000 refugees and migrants that have landed since the beginning of the year.

Tsipras said his government would speed up identification procedures to get migrants and refugees to the mainland as soon as possible.

At the moment, thousands who land on the eastern Aegean islands near Turkey are often forced to sleep in the open, with minimal access to hygiene, because local authorities have been overwhelmed by the sheer numbers.

Many of them are women and children -- including unaccompanied minors.

Tsipras also said he would hasten procedures to create a long-delayed state managing authority to unblock pending European support funds, a request reportedly put forward by European Migration Commissioner Dimitris Avramopoulos days ago.

The funds can be used for border protection and migrant integration, the PM said.

The Greek coastguard on Friday said nearly 55,000 people had illegally entered the country in July alone.

"The situation at the islands is dramatic, unprecedented," said President Prokopis Pavlopoulos, who was interior minister nearly a decade earlier.

"This flow of illegal migrants has never happened before," he said.

A new housing centre will soon be completed near central Athens to relocate hundreds of migrants currently sleeping in one of the capital's parks, Tsipras added.

"We aim to create a hospitable place where refugees can stay in dignified conditions," he said.

"We will do what we can to meet our humanistic obligation, by giving what little we have."

But he also criticised EU member states that have failed to fully implement migrant quotas suggested by Brussels or have rejected them altogether.

"The European Union has no other meaning if it is a union of states looking after their own interests," Tsipras said.

A senior immigration official said Greece had pledged to house 2,500 migrants and refugees by the end of the year.

The plan is "to create accommodation facilities around Greece for asylum applicants that we will eventually have," Vassilis Papadimitriou, general secretary for immigration at the interior ministry, told Athens 9.84 FM municipal radio.