The company said production averaged 25,597 barrels of oil equivalent per day (boepd).
It reiterated previous production guidance of between 25,000 boepd and 30,000 boepd for its full financial year.
Chief executive Amjad Bseisu said: "Production of 25,597 boepd to the end of April marks a good start to the year, reflecting strong reservoir and production efficiency performances from all of EnQuest's hubs."
The company reported that its key Kraken development project is "moving ahead according to plan".
Of the £595 million EnQuest expects to spend on developing new assets this year, £672m will be used on facilities for the Kraken heavy oil field east of Shetland, which it hopes to bring onstream by 2017.
EnQuest has a 60 per cent stake in Kraken.
It reported yesterday that the vessel for the project had arrived at a Singapore shipyard for conversion.
Earlier this month Cairn Energy, Enquest's partner in the Kraken field, revealed it had secured £340 million debt to fund its North Sea operations.
Previously legal problems had tied up cash expected from its Indian interests.
EnQuest said that first oil from the Alma field in the central North Sea is still expected in the second half of this year.
It has also secured a deal with Petroliam Nasional Berhad (Petronas), the national oil company for Malaysia, for development and production of the Tanjong Baram field offshore of Sarawak.