A regional governor in northern Greece has called for a state of emergency to be imposed on the border with Macedonia as the migrant crisis grows.
Apostolos Tzitzikostas, governor of Greece's Central Macedonia region, said the number of migrants on the frontier had grown to at least 13,000.
A state of emergency would facilitate aid supplies, Greek media report.
Earlier, the EU's top migration official warned Greece could be "overwhelmed" by the crisis.
Dimitris Avramopoulos, the commissioner for migration, told the BBC other states needed to support his country.
"Greece is overrun, is overwhelmed by all these flows," he said.
The migrants, most of whom entered Greece illegally by sea from Turkey, are seeking asylum in other EU states to the north.
Many are living in flimsy tents since they became stranded around the Idomeni border crossing, after EU countries re-imposed internal border controls and Macedonia sharply reduced the numbers allowed to cross.
More than 125,000 people have arrived on Greek shores so far this year, close to 12 times more than arrived in the first three months of 2015.
Many are believed to be fleeing conflict in Syria, Iraq and Afghanistan.
Mr Tzitzikostas, whose region shares the same name as the neighbouring country, said there were now 20,000 migrants in Central Macedonia as a whole – more than "60% of the country's entire refugee and migrant flow".
"We can no longer shoulder this strain by ourselves," he told Greek broadcaster Skai on a visit to Idomeni on Saturday to distribute humanitarian aid.
"It's a huge humanitarian crisis. I have asked the government to declare the area in a state of emergency. This cannot continue for much longer."
He also called on Macedonia, a republic of the former Yugoslavia seeking to join the EU, to open its borders immediately.
"The European Union needs to implement severe action against the countries that are closing borders today, whether they are members of the European Union or candidate members,'" he said.
"This is unacceptable what they are doing."
At least 2,000 new migrants are registered in Greece every day, most of them having made a hazardous journey by boat to the Greek islands off Turkey.
Earlier this week, EU officials announced an aid plan that would allocate €300m (£233m; $325m) this year to help EU states deal with the migration crisis.
The EU is to hold a summit with Turkey in Brussels on Monday to discuss further action to tackle the migrant crisis.
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.