Europe is “on the cusp of a largely self-induced humanitarian crisis” because of a rapid build-up of migrants on Greece’s borders, the UN has warned.
“The crowded conditions are leading to shortages of food, shelter, water and sanitation,” UN refugee agency (UNHCR) spokesman Adrian Edwards said.
Close to 24,000 migrants in Greece are in need of housing.
Some 8,500 of them are stuck in worsening conditions on the Greece-Macedonia border.
The crossing at Idomeni is now closed following protests by migrants desperate to continue their journey to Western European countries. Some migrants have been stranded at the overburdened camp for more than a week.
“At least 1,500 had spent the previous night in the open,” Mr Edwards said on Tuesday.
“Tensions have been building, fuelling violence and playing into the hands of people smugglers,” the spokesman added.
The site was beset by heavy rain overnight, posing serious health risks to a minority with no shelter.
BBC reporters saw hundreds more migrants heading across fields towards Idomeni on Tuesday.
Hundreds of small tents have been erected in the fields around the official camp, which can take no more people. Families of 10 are sharing four-man tents, Caroline Haga, an emergency co-ordinator for the International Red Cross (ICRC), told the BBC.
Ms Haga, who left the camp on Monday night but is due to return on Tuesday, said the medical charity had serious concerns for the health of the migrants as the weather deteriorated.
“Many people here are soaking wet and cold from having to sleep out in the open, it still dips below 10 here during the night,” she said.
“We are already seeing a lot of flu cases, especially among children, so imagine if they have to sleep outside in the wet again. It could turn into a very serious health problem.”
A medical station set up by the ICRC and Hungarian Red Cross was struggling to provide care for the large number of unwell and the pregnant, Ms Haga said, including people suffering from respiratory illnesses including bronchitis.
To make matters worse, a significant number of people were refusing to be taken away from the site for emergency care for fear of losing their place in the queue.
On Monday, a man suffering an epileptic fit refused to be moved, Ms Haga said.
Hassan Rasheed, 27, from Iraq, told the Associated Press: “I’ve been at Idomeni for 10 days, and it’s the fourth day I’ve been waiting to cross over.
“Conditions are very bad. There are many ill children who are coughing, and we spent the night in this tent under heavy rain.”
Ahmed Majid, a 26-year-old Iraqi travelling with his wife and two children, said: “We have been walking for three kilometres. Police stopped our taxi on the national road, which is why we are going through the fields.”
Macedonia was sporadically allowing few hundred people through the crossing, mostly Syrians and Iraqis, which was relieving pressure on the camp.
But last week it began refusing entry to Afghan migrants and imposing stricter document controls on Syrians and Iraqis, slowing the passage to a trickle.
Then on Monday Macedonia firmly closed the wire-mesh gate that separates it from the camp, citing the closure by Serbia of its northern border. A similar domino effect has been seen repeatedly over the past few months as Eastern European countries attempt to reduce the number of migrants within their borders.
Frustration at the closure boiled over on Monday and scores of migrants clashed with security guards. Some attempted to smash through a fence, prompting the guards to fire tear gas and rubber bullets.
Thousands of migrants and refugees are en route to Idomeni, despite the border closure. With the camp overwhelmed, many have been forced to wait on buses and at petrol stations along the route from Athens.
The Greek military has established three other border camps nearby to Idomeni, Ms Haga says, but all are already full, with about 2,000 people at each.