The measures announced in a statement from EU foreign ministers meeting in Brussels late Monday include:
suspending talks on an air transport agreement
a review of European Investment Bank lending
a reduction of financial assistance in 2020.
The ministers said additional "targeted measures" were being worked on to penalize Turkey, which began talks with the bloc to join the EU in 2005.
In recent weeks the bloc has become increasingly frustrated with Ankara's refusal to heed warnings after what the EU viewed as "illegal" gas drilling in Cyprus' exclusive economic zone.
Turkey does not recognize the government of the Republic of Cyprus.
The EU ministers called on Turkey to respect Cyprus' sovereign rights in line with international law and emphasized the "serious immediate negative impact" that Turkey's illegal actions were having on EU-Turkey relations.
The ministers also welcomed the Cypriot government's invitation to Turkey to negotiate the borders of their respective exclusive economic zones and continental shelf.
Two Turkish vessels escorted by warships are drilling for gas at each end of Cyprus.
Cyprus has been divided into the Republic of Cyprus, where people speak Greek, and a northern part under Turkish military control since 1974 when Turkey invaded in response to a coup by a Greek military junta.
The Turkish part is only recognized by Ankara, the predominantly Greek south is part of the EU.