Konica was born in Konitsa, today's Greece, back then part of the Janina Vilayet of the Ottoman Empire.

[2] After participating in the Congress of Lushnjë, he was appointed Foreign Minister once more and accompanied Fan Noli on his journey to the League of Nations.

[5] Although originally an opponent of Ahmet Zogu, Konica conducted negotiations in Rome on his behalf in 1926.

He served thereafter as an informal political advisor and intermediary and represented Albania at the Balkan Conferences of 1931.

[6] During World War II, Mehmed bey Konica was initially interned in Rome by the Italians and, later, under the German occupation, was appointed Albanian Foreign Minister but refused to take up the position.