The daily flow from Shah Deniz to Turkey before the increase was 10-11 million cubic metres. BP-Azerbaijan is the operator of Shah Deniz, which produces about 25 million cubic metres of gas per day.
This follows an increase in gas supplies to Turkey from Russian group Gazprom after saboteurs bombed a gas pipeline in eastern Turkey on Friday, halting the flow of Iranian gas and causing minor injuries to 28 Turkish soldiers.
Turkish energy minister Taner Yildiz said the line would be back in operation soon, but gave no timetable.
Gazprom Export said on Friday it had met a request from Botas to increase supply via the underwater Blue Stream pipeline to a daily 48 million cubic metres from 32 million.
Turkey is Gazprom's second-largest natural gas consumer after Germany.
The outlawed Kurdistan Workers' Party (PKK) has claimed responsibility for repeated attacks on pipelines in Turkey in its 28-year-old armed campaign for Kurdish self-governance which has intensified over the last few months.