Mr Gilmore was speaking after a meeting with a group of retired international leaders, The Elders.
Former US President Jimmy Carter said he was encouraged by a meeting this morning.
Mr Carter was at a meeting at the Department of Foreign Affairs with representatives of 20 EU states, who unanimously supported the labelling move.
Former President Mary Robinson, another member of The Elders, said they were not happy that the EU just “talks the talk” and said they wanted to see practical steps.
Mr Gilmore said work was under way at EU level to introduce labelling, and it would clearly be more effective if it was done at European level.
However, he said the Government had a process in train to do it unilaterally if necessary.
Former South African President Nelson Mandela is an Honorary Elder.