Turkey's "unlawful activities. should be immediately terminated", he said, adding however that he conveyed Cyprus' support for resolving disputes in the eastern Mediterranean through dialogue.
Erdogan also said France has no right to criticise Turkey, considering its colonial record.
Macron's statements came during an informal summit with southern European Union countries, who also warned Turkey against "unilateral activities" in the eastern Mediterranean.
In a message on NAVTEX, the global maritime navigational telex system, Turkey said on Friday there would be a gunnery exercise off the coast of Sadrazamkoy in northern Cyprus.
Ahead of an EU summit from 24 to 25 September, where the issue will be raised, tensions have hit fever pitch between North Atlantic Treaty Organisation member Turkey and southern European states over hydrocarbon extraction in the eastern Mediterranean.
The Oruc is supposed to remain in the disputed waters until Saturday, but the Turkish Yavuz drillship will remain in the contested waters until 15 September, and will soon be joined by the Kanuni exploration vessel.
The Turkish-Greek tensions in the Eastern Mediterranean escalated after Ankara began exploration drilling in the Greek-claimed waters in early August.
Pompeo met the Cypriot officials after a trip to Doha where he inaugurated long-awaited talks between Afghanistan's government and the Taliban.
The dispute "has to be resolved in a way that's diplomatic and peaceful", Pompeo told reporters on his plane.
Mitsotakis is believed to have hammered out the programme announced on Saturday after talks with French President Emmanuel Macron during a southern European leaders summit in Corsica this week.
Ahead of his visit to Cyprus, US Secretary of State Mike Pompeo called for Turkey to withdraw its forces from the East Mediterranean, news agencies reported on Friday. "So, I'll be working on that project as well, trying to make sure that I understand the risks that are associated from the people of Cyprus' perspective".
Turkey - the country with the longest coastline on the Mediterranean - has sent out drill ships to explore for energy on its continental shelf, saying that both Turkey and the Turkish Republic of Northern Cyprus have rights in the region.
In order to reduce tensions, Turkey has called for dialogue to ensure fair sharing of resources.