EU officials have pledged millions of euros of financial assistance to Greece to help tackle a migration surge from neighbouring Turkey, warning against those wishing to "test Europe's unity".

Flying by helicopter over the Greece-Turkey border, where thousands of desperate asylum seekers have tried to break through for days, European Commission President Ursula von der Leyen said on Tuesday the bloc would provide Greece "all the support needed".

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"Those who seek to test Europe's unity will be disappointed. We will hold the line and our unity will prevail," von der Leyen said, standing alongside Greek Prime Minister Kyriakos Mitsotakis and the chiefs of the European Council and European Parliament.

Von der Leyen said the bloc would provide 700 million euros ($777m), half of it immediately, to help manage the refugee situation.

In addition, the EU border agency Frontex will deploy a rapid intervention team including an additional 100 guards backed by coastal patrol vessels, helicopters and vehicles, she said.

"Our first priority is making sure that order is maintained at the Greek external border, which is also the European border," von der Leyen told journalists.

'Wake-up call' for Europe

Earlier, Mitsotakis announced that Greek border forces had averted "over 24,000 attempts at illegal entry" by land and sea, making dozens of arrests.

"Europe has not been up to the task of dealing with the migration crisis," he said.

"I hope this crisis will serve as a wake-up call for everyone to assume their responsibilities."

Amid claims on the Turkish side that Greek security forces are shooting near refugees and migrants, European Council President Charles Michel said it was "crucial to act in a proportionate manner and to show respect for human dignity and international law".

At the Greek border crossing of Kastanies, reporters with the AFP news agency saw soldiers boarding refugees and migrants onto military vehicles. Other unmarked vans were also picking up people wandering on the streets.

Thousands have arrived at the frontier since President Recep Tayyip Erdogan announced last week that Turkey would no longer stop them trying to enter Europe.

European leaders have insisted Ankara abide by a 2016 deal to stop departures in exchange for six billion euros in assistance.

"Our first priority is making sure that order is maintained at Greece’s external border, which is also Europe’s border." President @vonderleyen pic.twitter.com/qU8tcZ9v0h — European Commission 🇪🇺 (@EU_Commission) March 3, 2020

Von der Leyen said she had "compassion for the migrants that have been lured through false promises into this desperate situation."

Turkey is the world's largest host of refugees - about four million, and faces another influx from Syria where the government, backed by Russian air power, is pressing a violent offensive to retake the last rebel-held province of Idlib.

Erdogan had previously warned that he would open the gates, accusing the EU of not fulfilling its promises.

"We have been calling for a more equitable burden and responsibility-sharing for a long time," Hami Aksoy, the Turkish foreign ministry spokesman, told Al Jazeera.

"All our efforts contributed significantly to the security of Europe. However, our calls were ignored by the EU and member states."