The two southern European countries that absorb nearly all boat-borne refugees from North Africa and Turkey are taking steps to halt the arrivals, with both saying they have reached their limit.

The United Nation’s International Organization for Migration reports that 20,484 migrants and refugees entered Europe by sea this year through mid-March. More than 80 percent – 16,248 -- of that staggering number arrived in Italy, the second largest-number went to Greece and the third-largest to Spain.

Greek Migration Policy Minister Yannis Mouzalas said that his nation is not able to absorb any more and will not be taking any more refugees.

He said that Greece is unable to abide by the Dublin Regulation, which holds that refugees may be sent back to the first European stop they made.

"We accommodate 60,000 refugees … and it would be a mistake to make Greece’s burden heavier by the revival of the Dublin agreement," Mouzalas told German newspaper Spiegel in an article that was published Sunday.

Mouzalas said Greece is coming out of its economic hardship and cannot take on more of a burden.

“Greece simply has no capacities to cope with additional arrival of refugees," he said. "We've just pulled ourselves together, so please, don't make us falter again."

Meanwhile, officials in Italy, which has received about 500,000 migrants in the last three years, say that rescue vessels operated by charities and humanitarian organizations – some of which reportedly receive funding from billionaire George Soros and his Open Society Foundations (OSF) -- are working with smugglers based in Libya.

Greece simply has no capabilities to cope with additional arrival of refugees. We've just pulled ourselves together, so please, don't make us falter again. — Greek Migration Policy Minister Yannis Mouzalas

OSF emphatically denies such accusations.

"Our grantees and our partners do not help people cross borders, neither within nor into the European Union," an OSF spokesperson told Fox News. "Our work aims both to support effective and orderly government migration policies and to ensure that the rights of migrants are upheld in accordance with domestic and international law."

Italian officials also say that some NGOs act as a sort of “taxi service” by picking refugees up just off the African coast and then transporting them across the Mediterranean Sea to Italy instead of returning them to Africa.

Whomever is resonsible, an Italian lawmaker said that groups transporting refugees should take them to closer places such as Malta and Tunisia.

Other Italian authorities want to investigate the funding of charity boats transporting the migrants. Critics of the charity boat operators say they are colluding with criminal smugglers and, in effect, are accomplices in the deaths of so many migrants trying to reach Europe.

“If the government does not decide to put a brake on these [humanitarian] boats, we will find ourselves overrun by tens of thousands of African immigrants by the end of the year,” said Paolo Grimoldi, a lawmaker who belongs to the Northern League party, according to Reuters.

GEFIRA, which stands for the Global Analysis from the European Perspective, questioned on its website whether the smuggling involving humanitarian organizations, local smugglers and even the Italian Coast Guard rise to the level of a criminal enterprise.

“The Dutch, Maltese and German-based NGOs are part of the human smuggling network and one wonders, are these NGOs themselves criminal organizations?” asked GEFIRA. “Whatever the motives of these NGOs, their behavior is illegal, and in countries governed by a constitution, i.e. European states, crimes should be prosecuted regardless of the intention of its perpetrators.”

The charities deny they are doing anything wrong and say they are in fact helping to save lives by getting migrants out of dangerous zones.

Migrants have described Libya as increasingly dangerous because of violence between factions fighting for power. They say smugglers are also operating in a kind of anarchy since former leader Muammar Gaddafi was overthrown six years ago.

Over the weekend, humanitarian ships rescued more than 1,000 Italy-bound people on the Mediterranean Sea on crowded boats, according to Doctors Without Borders, who were quoted in several published reports.

Since January at least 481 people have died attempting to reach Italy.