The bottlenecks have overwhelmed many of the camps, especially on the Greek islands, where migrants arriving after the March 20 deal are supposed to be held until being deported to Turkey. That program has stalled because of legal challenges and because Greece must process each asylum application first. So far, 468 of the more than 10,000 people who have arrived since the deal took effect have been returned. Turkish monitors assigned to assist were fired by President Recep Tayyip Erdogan of Turkey after the coup attempt against him.

One result is that on Lesbos, the main landing point for dinghies arriving from Turkey, the Moria refugee camp is brimming with Syrians, Afghans, Eritreans, Pakistanis, Kurds and others who landed after the accord. While the camp is organized by the Greek military and police, and filled with humanitarian aid workers, it has grown increasingly overcrowded amid a backlog of asylum claims and bids to enter the European Union relocation program.

As in Nea Kavala, migrants in Moria had no clue about their status.

“We just wait and we don’t know what to do,” said Abdullah Jalali, 40, an Afghan who had been stuck for five months.

His family was crammed with 30 other people, including 11 babies, into a tiny container shelter. Nearby, Pakistani migrants lived outside beneath tarps held up with metal parking barriers — dark cages in the baking sun.

Mr. Erdogan has set off further alarms by hinting that the European Union deal could collapse by October should Europe fail to uphold a part of the bargain to grant Turkish citizens visa-free travel to Europe. The situation is critical enough that Prime Minister Alexis Tsipras of Greece met with his cabinet on Thursday in Athens to discuss how to handle a renewed migrant surge.

For those who had been languishing in Greece even before the deal, Europe’s political tug of war threatens to make a precarious situation worse. Those who have money are continuing to turn to smugglers for passage to Germany or the Nordic countries. Some Syrians who fled violence for a haven in Europe have decided to return rather than face an indefinite stay in the camps.