The foreign affairs minister raised the issue with his EU counterparts at the Foreign Affairs Council in Luxembourg, where he also met the Burmese opposition leader, Aung San Suu Kyi.
Violence in Syria, Libya, and Egypt — where three sisters and one brother from the Dublin-based Halawa family are being detained — were on the agenda.
Mr Gilmore said he specifically raised the situation of the members of the Halawa family, who were arrested in August, as he had become “increasingly concerned” about them.
Sisters Omaima, 20, Fatima, 22, and Somaia, 27, and their 17-year-old brother Ibrihim had travelled to Egypt in the summer for a holiday.
Mr Gilmore said no specific charges have been brought before them and that their detention has been extended a number of occasions, the last time for a period of 45 days.
The four were forced to seek sanctuary in the Al Fateh mosque in mid-August after violent clashes between supporters of ousted president Mohammed Morsi andthe security forces.
They were subsequently jailed in Tora prison and last appeared before the prosecutor’s office at the end of September.
The Department of Foreign Affairs has been providing consular assistance to the siblings, from Firhouse, south Dublin.
The Foreign Affairs Council, a meeting of all 28 EU foreign ministers, also discussed Myanmar following the decision to lift all EU sanctions.
Mr Gilmore said: “We have worked on that issue since then, our officials have been involved in scoping out an aid programme, and I expect to be in a position shortly to announce details of an Irish Aid programme in Myanmar/Burma which will help in the transition to democracy.”