ATHENS — Greece and the European Union scrambled on Sunday to put in place the people and the facilities needed to carry out a new deal intended to address the migrant crisis that is roiling Europe, as hundreds of migrants in rubber dinghies continued to land on the Greek islands from Turkey.

The accord, struck between the union and Turkey on Friday, set a 12:01 a.m. Sunday deadline for Turkey to stem the flow of people making clandestine journeys across the Aegean Sea to Greece in an attempt to enter Europe, and required Greece to begin sending back migrants who are not eligible for asylum.

Yet processing centers on the Greek island of Lesbos and on several other Greek islands were not adequately staffed to comply immediately with the new measures, and officials said they were waiting for the European Union to follow through on a pledge to send at least 2,300 European police and asylum experts to help.