I agree the General Affairs Council has a supervisory role. Title six of the Treaty on European Union provides a framework for co-operation within the Union in the fields of justice and home affairs, including immigration policy and policy regarding nationals of third countries. The General Affairs Council retains overall responsibility for the external relations of the Union and in this context can discuss pertinent political or humanitarian aspects where large numbers of people are fleeing a country.
However, substantive responsibility for immigration falls within the remit of Ministers for Justice and Home Affairs. A discussion took place at the General Affairs Council meeting on 8 December last when Ministers exchanged views on political aspects of the influx of immigrants from Northern Iraq, taking account of the debate at the Justice and Home Affairs Council on 4 December. The Council mandated COREPER to consider the matter and Ministers agreed to take it up at a future meeting with a view to debating the underlying causes of the influx of refugees.
Also at the meeting on 8 December, Ministers had an informal and inclusive discussion over lunch about the requirement of Bulgarian and Romanian nationals to secure visas for entry to the EU. Similar aspects have been discussed in the cases of former Yugoslavia and Albania. This is not an exhaustive list of discussions which may have taken place over the years at the General Affairs Council. An annual report on achievements in the field of justice and home affairs is submitted to the General Affairs Council and then to the European Council.