The Greek coastguard said today that at least three people died after a boat carrying dozens of immigrants ran aground off the island of Rhodes. Video footage and photos posted by a local news website show a large, wooden double-masted boat, packed with people, just metres from the land.

The vessel rocks wildly in the waves and passengers are seen in a photo jumping into the sea and swimming toward land.

Libyan smugglers are telling migrants to remain stationary during trips to Europe, in full knowledge that even small movements of such overpacked boats could overbalance and capsize the vessels. According to a Libyan fisherman from a major smuggling hub in west Libya, the ships that capsized with catastrophic effect in recent days did so because migrants ignored instructions to stay put once on board.

"When they leave, they are told to stay where they're seated," said the fisherman. "Then at daybreak they realise they're in the midst of the ocean, they start to shift around, and then the boat, which can only withstand a certain number of tons, has its balance shifted. It starts to take on water and begins to sink."

Before Sunday's disaster, the International Organisation for migration estimated that about 20,000 migrants had reached the Italian coast this year, and 900 had died.

There will be tough words in Luxembourg about clamping down on the criminal networks of people-traffickers in Libya and elsewhere in north Africa and about the need to tackle the roots of the migration epidemic at source in the Middle East and sub-Saharan Africa.

But European governments, deeply divided over how to respond, appear impotent in the face of the surge of migrants risking their lives to reach European shores, and are reluctant to relax immigration policies for fear of boosting support at home for anti-immigrant parties doing well in many parts of the union.

The populist anti-immigrant Finns party, formerly the True Finns, performed strongly in general elections on Sunday, coming second and are likely to be part of the new government in Helsinki. Three weeks before Britain's election, Theresa May, the home secretary, will be unlikely to risk any policy shifts that might bolster Nigel Farage and his anti-immigration UK Independence party. Thomas de Maizière, the German interior minister and chancellor Angela Merkel's former chief of staff, also takes a hard line, arguing, like May, that more ambitious European search-and-rescue missions in the Mediterranean will act as a "pull factor", encouraging smugglers to send more migrants to sea in unsafe, packed vessels.

The national governments of Europe, as opposed to the EU institutions in Brussels, are responsible almost entirely for immigration policy and jealously guard their national prerogatives. Dimitris Avramopoulos, the European commissioner responsible for migration issues, will attend the Luxembourg meeting. He is to unveil a new EU policy blueprint next month, but power rests overwhelmingly in national capitals.

While the ministers are unlikely to agree on any swift, concerted action to mitigate the problem, the EU's failure to mount effective naval patrols charged with saving lives is being loudly condemned as a scandal. Munich's Süddeutsche Zeitung at the weekend denounced the EU as a "union of murderers", accepting the deaths of refugees in the hope of discouraging other refugees from following them.

The crisis has put the spotlight on the Italian prime minister, Matteo Renzi,who on Sunday issued a harsh critique of his European partners for not assisting Italy as it tries to cope with the influx of migrants. The centre-left politician called the traffickers the "slave drivers" of the 21st century. He has insisted for months that the solution to the problem was not increasing patrols at sea, but instead focusing international efforts on returning stability to Libya.