The refugees' objective is Lesbos' main port, Mytilini - the only place where the Greek authorities will grant them the permits that will allow them to travel by ferry to Athens and continue their journey through the Balkans towards Western Europe.
It is a punishing march for people who have already been on the move for weeks, leaving wartorn countries such as Syria and Iraq, travelling through Turkey and waiting for days for smugglers to ferry them across the narrow strait.
"We've been walking since 11am yesterday," said Razan Al Asfar, 28, in sweltering temperatures with her two small children - Hala, 6, wearing a My Little Pony T-shirt, and Omar, 4. The children were exhausted in the 35C summer heat, nibbling on dry crackers and drinking warm water from a plastic bottle.
"We've walked 15km but we have another 40km to go," said Al Asfar, who used to work as a pharmacist in the Syrian city of Hama before fleeing the civil war.
She paid smugglers US$2400 ($3817) to ferry her and her children across the sea from Turkey in an inflatable boat. "The smugglers threw all our things into the water so they could squeeze more people into the boat. I lost everything - bags of clothes for the children, and some food."
Greece's Immigration Minister has warned that Lesbos - which has received 50 per cent of the 230,000 refugees who have reached Greece so far this year - is "on the verge of explosion". Yiannis Mouzalas said there were up to 17,000 refugees living in squalid conditions in Mytilini. He said more ferries would be laid on to start transporting refugees to Athens from a second port on the island, Sygri, to ease the pressure.
Refugees who were initially grateful to have arrived on Lesbos are now increasingly angry at the delays - some of them have been sleeping on the streets of Mytilini for two weeks. In a makeshift camp outside Mytilini, refugees tried to burn down a temporary structure as a protest against the delays in being registered.
"Until now we really respected the Greek people but I fear that if the situation goes on like this, there will be violence - refugees will start smashing cars, even killing people," said Marah Al Darwish, 24, a Kurd from Aleppo.
Refugees mill around the town, dozing through the hottest hours of the day, trying to entertain their hungry children and camping out beside yachts in the harbour as tourists enjoy meals in the tavernas.
They queue for hours outside the registration office - a metal container - only to be told to go elsewhere, or to come back the next day.
The islanders of Lesbos say they simply cannot cope with the influx. "It's a tsunami - the numbers are just too much," said Stratos Kalpakis, 50.
Athens has asked the European Union to activate its crisis response mechanism to provide staff, medical supplies, clothes and equipment.
Describing the situation on Lesbos as "wretched", Mouzalas, the minister, said the Government planned to remove 12,000 refugees from the island over the next five days by increasing the number of ships ferrying people to Athens from three to four or five.
Hungary
Scores of refugees broke through a police line near a refugee centre and marched against oncoming traffic on a motorway, headed for Budapest. The group of around 200 walked about 15km before police persuaded them to board buses to a nearby registration camp for asylum-seekers.
Denmark
The Danish Government has placed an advertisement in newspapers in Lebanon which carries an unspoken message: Don't come to Denmark. The advertisement lists a number of factors that would make Denmark an undesirable destination, including one recent change to legislation that would reduce social benefits to arriving refugees by 50 per cent.
Australia
Australia's response to the Syrian crisis will involve offering temporary and permanent refuge, Foreign Minister Julie Bishop says. Immigration Minister Peter Dutton has provided an initial report to the Government on his talks in Paris with United Nations officials.
Britain
Twenty thousand Syrians will be give new homes in Britain over the next five years, according to Prime Minister David Cameron. He said that a total of 4000 a year would be admitted over the next five years. Orphans would be given priority. Telegraph Group Ltd,
- AFP, AAP
