Eni said it had signed a memorandum agreeing "to explore the possibility of extending Eni's activities to Turkmenistan's offshore sector of the Caspian Sea."
The Italian oil and gas group also agreed to extend its operations in the Nebit Dag onshore area until 2032.
"These strategic agreements strengthen Eni's presence in Turkmenistan," the company said.
The agreements were signed after Italy's Prime Minister Matteo Renzi - making the first ever visit to Turkmenistan by an Italian premier - held talks with President Gurbanguly Berdymukhamedov.
The agreements came as the European Union is intensifying efforts to reduce its energy dependence on Russia amid a confrontation over the Ukraine crisis.
Turkmenistan, on the eastern shores of the landlocked Caspian Sea, claims to hold the world's fourth-biggest reserves of natural gas.
"In our foreign policy, Turkmenistan's priority is cooperation with the European Union and we want to see Italy as our main partner in carrying out our agreements," Berdymukhamedov said during talks with Renzi.
"Today we signed a package of documents that will continue the work of Eni in Turkmenistan," Berdymukhamedov told journalists after the meeting in the capital Ashgabat.
"Now it is working in four [onshore] oilfields," he said, estimating investments at $1.6 billion (€1.28 billion).
Referring to the second agreement, Eni "has legally become the main operator" at Nebit Dag and extended its operations by a decade, Berdymukhamedov said.
Turkmenistan and Eni will look into "the possibility of exploration and extraction" in two blocks of Turkmenistan's sector of the Caspian Sea, believed to contain 510 million tonnes of oil and 600 billion cubic metres of gas, Berdymukhamedov said.
Germany's RWE is already carrying out exploration in Turkmenistan's sector, which is also being developed by Dubai-based Dragon Oil and Malaysia's Petronas.
Turkmenistan's energy reserves have prompted a hugely ambitious $7.5 billion project to build a 1,800 kilometre pipeline throug Turkmenistan, Afghanistan, Pakistan and India, called Tapi, sparking interest from international energy giants despite the logistical difficulties.