The Aphrodite field is mostly on the Cypriot side of the maritime border, but some of it lies within Israel's economic zone.
The two countries are at odds over how much gas is likely to be on the Israeli side, Lakkotrypis said.
"We have recently agreed to ask companies first to try to reach a settlement between them as regards the quantities that may be in the Israeli area," he said.
"If this is not possible then we will go to arbitration."
US firm Noble Energy in 2011 made the first gas find in the Aphrodite field (Block 12), which is estimated to contain around 127.4 billion cubic metres (4.54 trillion cubic feet) of gas.
Lakkotrypis said talks were underway in good faith to determine how far the field extends into the area under Israeli jurisdiction.
He said energy firms Noble Energy, Shell and Delek would discuss the issue with Israel Opportunity Energy Resources.
If they cannot agree, they will refer the question to experts, he said.
Energy will be on the agenda when Israeli Prime Minister Benjamin Netanyahu meets Cypriot President Nicos Anastasiades in Nicosia next week, along with Greek premier Alexis Tsipras.
Israel and Cyprus signed a deal on the border between their exclusive economic zones in 2010, but they did not reach an agreement on how to deal with their shared gas fields.
Cyprus is in advanced talks with Cairo with a view to exporting natural gas from the Aphrodite field to Egypt.
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