“We were anchored for the night and woke up to screaming and shouting at about three or four in the morning,” Carlotta Dazzi, a journalist and sailing instructor told La Repubblica.
“We went outside and saw a huge rubber dinghy against the rocks, far from the beach. You could tell by the voices that many of them were children. We went out and did what anyone would have done.”
Out of the 15 or so boats that were anchored in the area, theirs was the only one that moved to help, Dazzi said.
The couple fed the migrants what they had on the boat, “water, biscuits, crackers bread...”, Dazzi said, until Greek people arrived as the sun rose, bringing "grapes, figs..."
“The Greeks have been fantastic, very welcoming, it's Europe that sucks."
Dazzi added that “a couple of hundred” migrants arrive on the island, which lies a short distance from Turkey, each day, but the local authorities "no longer know where to put them".
Despite the warmth of ordinary islanders, Dazzi's story emerged as police on Kos on Tuesday beat migrants with truncheons and sprayed them with fire extinguishers as its mayor, Giorgos Kiritsis, warned of a "bloodbath" if the migrant crisis gets worse.
And amid mounting tensions across Europe over the spike in new arrivals, Germany's police union called for a scrapping of Europe's visa-free Schengen travel zone - while Italian police said they had arrested nearly 900 suspected human traffickers since January 2014, but added that the kingpins were at large.
In Kos, the migrants, mostly Afghans and Syrians, were being relocated to a local football stadium after camping along roads and beaches for weeks.
Four police used truncheons and fire extinguishers seemingly to prevent a stampede as a crowd tried to squeeze through a door into the stadium, an AFP photographer at the scene said.
At least one woman had fainted in the heat and many children were crying as the tightly packed mass of people jostled for space, just days after the country's handling of migrants came under fire from the United Nations.
Tensions on the tourist island are high with its mayor claiming there were 7,000 migrants stranded on Kos, which has a population of only 30,000 people.
On Monday, a Kos police officer was suspended after being filmed slapping and shoving migrants queueing outside the local police station as they waited to be documented so they could go on to Athens.
A police source in Athens told AFP that the latest incident occurred because the migrants were trying to get into a police post to get their papers sorted, but the officers wanted to process them inside the stadium.
Greek Prime Minister Alexis Tsipras last week said the refugee crisis "surpasses" his crisis-hit nation's resources and called for European Union assistance.
'Scrap visa-free travel regime'
In Germany, the police union meanwhile called for the reintroduction of internal European border controls and sought more personnel to deal with a record flood of refugees.
"From a policing point of view, a return to border controls would be the best of all measures," said Rainer Wendt, chairman of the German Police Union, in a newspaper interview.
In EU talks on the wider refugee crisis, "Germany should not take the threat of bringing back (border) controls off the table too readily," Wendt told the Passauer Neue Presse.
Europe has abolished passport controls within the so-called Schengen zone, which incorporates 22 EU members as well as Switzerland, Norway, Iceland and Liechtenstein.
However, police have stepped up spot checks of travellers on inter-European trains, highways and flights.
Meanwhile in Italy, which is the main point of entry for migrants trying to reach Europe by sea, the coastguard said they had rescued about 170 people travelling in two rubber dinghies off the Libyan coast.
Several news outlets including the Ansa news agency said the second dinghy was about to sink after becoming deflated when an Italian naval helicopter intervened. They said up to 50 passengers on this boat were feared missing.
Italian authorities have been trying to identify people traffickers mixed in among the migrants.
Police data show that 888 suspected people traffickers have been arrested since January 2014.
Of those arrested, the majority are small-time operators from Egypt and Tunisia, data published in the Catholic daily Avvenire showed.
Despite increased police cooperation between Italy and the countries concerned -- with the exception of war-torn Libya - none of the internationally-sought trafficking masterminds have been arrested, it said.