Athens accused Erdogan of fueling tension in the region.
The president of the company, Claudio Descalzi, declared from Cairo that he trusted in a solution of the problem because "we are well inside the Economic Zone of Cyprus" where' we have drilled other wells under the same conditions ... and nothing absolutely happened ', said quoted by the agency ANSA.
Turkey faced criticism Monday after its warships continued to impede a rig from reaching a location off Cyprus where Italian energy company Eni is scheduled to drill for gas.
Cyprus government spokesman Nicos Christodoulides told state broadcaster RIK that the rig remained anchored in the eastern Mediterranean, about 50 kilometers (30 miles) from the drilling target off the southeastern coast.
Turkey opposes the oil drilling, saying it disregards the rights of breakaway Turkish Cypriots.
Turkish President Recep Tayyip Erdogan has issued a warning to Greece, Cyprus and worldwide companies exploring for gas in the Mediterranean not to "step out of line" and encroach on Turkey's rights.More news: Kim Kardashian West exhibits her tiniest waist till now at 24 Inches
The Italian drilling platform Saipem 12000 is still being held today in the area where it was intercepted three days ago by Turkish naval units, when it was heading to Cyprus to perform work in a gas field.
On Monday Greece accused Turkey of violating global law and said its "provocative conduct" was inconsistent with that of a country seeking accession to the EU.
Greece's Foreign Ministry has condemned what it calls Turkey's "blatant violation" of Cyprus' sovereign rights, as well as its disregard for worldwide law.
"The EU stresses the need to respect the sovereignty of member states over their territorial sea and airspace", she added, also with reference to regular Turkish incursions in Greek sea and airspace.
"(Turkey) is not helping to smooth out the turbulence, it's doing the opposite", he said.
Cyprus became a member of the European Union in 2004, but only the southern part of the island enjoys full benefits.
In 1996, the dispute over territorial possession of the two rocky islets of Imia in the Dodecanese archipelago in the Aegean Sea led to a crisis in relations between Greece and Turkey.