Shares in Genel, which have fallen more than 92 percent since its peak in 2014, were down 3.2 percent at 84.50 pence in early trading.
The oil producer said it would target further investment in Taq Taq, and cautioned that "it remains too early to extrapolate long-term conclusions" from oil field's production trends.
Genel co-founder Nathaniel Rothschild quit on Monday, joining co-founder Tony Hayward, and chief financial officer Ben Monaghan, who have announced plans to depart.
Hayward, formerly chief executive of BP, said in the company's statement that its board composition is under review. He will retire from the board on Tuesday.
Genel shares have plunged after two downgrades to reserves at Taq Taq, failed exploration campaigns in Africa, political unrest in Iraq and a sharp drop in oil prices since 2014.
Under Chief Executive Murat Ozgul, who took over from Hayward in 2015, Genel is focused on retrieving money it says it is owed by the Kurdistan Regional Government (KRG) for oil it has sold and on finding a partner to develop two gas fields in the region, with the aim of linking them to neighbouring Turkey.
"The economic situation in the Kurdistan Region of Iraq continues to improve," Hayward said on Tuesday, adding that the KRG has made gross payments of $316 million so far this year. Genel said it has now received oil export payments for 18 consecutive months, adding it expects to continue receiving payments.
The company also said its Tawke field in Iraqi Kurdistan continued to perform in line with expectations, while it expects the Peshkabir field, situated west of Tawke, to add to production from the end of 2017.
Net production averaged 37,700 barrels of oil per day (bopd) in the year to May 31, with average production from Taq Taq of 23,300 bopd, Genel said.
(Reporting by Arathy S Nair in Bengaluru; editing by Jason Neely and Louise Heavens)