Dubbed Operation Claw-Lock, the Ankara government says the offensive is a pre-emptive measure to prevent the PKK from using Iraq as a base to carry out attacks in Turkey.
Founded in 1984 to fight for Kurdish self-rule, the PKK is designated as a terrorist organization by Turkey, the United States and the European Union.
The new operation comes days after Iraqi Kurdistan Prime Minister Masrour Barzani met with Turkish President Recep Tayyip Erdogan in Ankara. The two leaders discussed ways to improve security, business and trade ties, according to a statement by Barzani's office.
Turkish Defense Minister Hulusi Akar was quoted by the state-owned Anadolu news agency as saying, "Our operation is continuing successfully as planned. The targets identified in the first phase have been captured."
Meanwhile, in a statement, the PKK fighters claimed to have downed two Turkish helicopters and killed more than two dozen Turkish soldiers.
VOA cannot independently verify the conflicting reports.
The Turkish military has carried out several operations against the PKK in recent years, both inside Turkey and in northern Iraq. The latest operation targets areas near Amedi city's Shiladze district.
Amedi's mayor, Warsheen Mayi, told VOA by phone that the operation has not targeted civilian areas. But Iqbal Omer, a freelance journalist, said civilian properties had been damaged in the most recent airstrike.
Turkish interests in northern Iraq go beyond combating the PKK. Turkey has a significant economic stake in the region, particularly the energy sector. Turkey is also seeking to expand its influence in the region as a counterbalance to the growing power of Iran.
Some experts have suggested that Kurdistan, which is estimated to have 700 billion cubic meters [25 trillion cubic feet] of natural gas, could become a major energy supplier to Turkey and Europe as the world tries to wane itself off its dependence on Russian gas.
"Europeans are searching for new potentials to supply gas to Europe," said Nahro Zagros, a non-resident senior fellow at the Washington-based Gold Institute for International Strategy.
"The KRG (Kurdistan Regional Government) can be one of these potentials. Having said that the KRG cannot fill the whole vacuum that Russians will leave in Europe, but it can help in some ways, and this cannot be achieved without Turkish support," he added.
Safeen Dizayee, head of the KRG's Department of Foreign Relations, said that after meeting domestic supply, his government was open to the notion of exporting natural gas to Europe.
"The Kurdistan region is not trying to become an alternative to other countries," he told VOA. "That is why it will in the first stage use most of its extracted gas to supply domestic needs. Later on, some portion of the gas can be exported to other parts of Iraq if they have a need for it. In the coming years, when the Kurdistan region opens up more to the world, no doubt it might export some of the gas."
Dizayee added that Turkey, which serves as a bridge for the landlocked Kurdistan region to the outside world, will be a major partner in the exportation of gas.
Others, such as Sulaymaniyah-based Izzat Sabir, an economist who led the Finance and Economic Committee in the Kurdistan parliament, say the region first needs to resolve its internal political issues and meet domestic demand before it can focus on becoming an exporter.
Not every Kurdish politician is on board with the idea of exporting the region's gas through Turkey.
"I think it's my party's official decision that we will not allow natural gas to be sold through Turkey the way oil is being sold," said Rekawt Zaki, a senior leader of the Patriotic Union of Kurdistan (PUK), which controls some of the region's largest gas fields in Chamchamal.
"The future of the Kurdistan Region is natural gas, not crude oil. Crude is depleting in many fields," economist Sabir said.
"Iraq imports billions of dollars' worth of natural gas from Iran and other neighboring countries. While the domestic demand for gas has not been met, we in the Kurdistan region should not think about signing agreements to export natural gas," Sabir added.
Mutlu Civiroglu, Zhiyar Mohammed, and Rikar Hussein contributed to this story from Washington. This story originated in VOA's Kurdish Service.
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