NEW YORK, April 12 (Reuters) - The U.S. Permian basin has not seen peak production, and increases in output from the region will help to offset production declines in other basins going forward, said Occidental Petroleum Chief Executive Vicki Hollub on Wednesday.

Crude output in the Permian basin in Texas and New Mexico, the biggest U.S. shale oil basin, is expected to rise to 5.62 million barrels per day this month, according to estimates from the U.S. Energy Information Administration.

While the projection would be a record high, oil output from the region is expected to gain by 26,000 bpd from March, the smallest increase since last December, EIA data showed.

Oil prices have surged above $80 since the beginning of the month, after the Organization of the Petroleum Exporting Countries and allies including Russia, collectively known as OPEC+, surprised markets with an announcement of voluntary production cuts of 1.66 million barrels per day (bpd) from May until the end of 2023.

Pioneer Natural Resources chief executive Scott Sheffield said Wednesday that if oil prices break above $90 per barrel, then prices will likely reach $100 per barrel this year. Sheffield estimated that prices would then remain in a range of $90-$100 a barrel for some time.

OPEC+'s surprise output cut was to maintain a balance between supply and demand, said Kuwait Petroleum Corporation Chief Executive Shaikh Nawaf S. Al-Sabah. (Reporting by Laura Sanicola and Stephanie Kelly; Editing by Chris Reese and Daniel Wallis)