* April daily output soars to highest since May 2014
* Mills ramp up production after winter curbs lifted in mid-March
* Coke output was highest since Sept 2017 (Adds comment, background)
BEIJING, May 15 (Reuters) - China's daily crude steel output in April rose to its highest in at least 4 years, official data showed on Tuesday, as mills boosted production to take advantage of high margins after the end of winter output curbs.
Overall steel output in the world's top producer climbed to 76.7 million tonnes in April, up 3.7 percent from March and up 4.8 percent from April a year ago, according to data from the National Bureau of Statistics (NBS).
Daily average output reached 2.56 million tonnes last month, the strongest since at least May 2014.
The rise came after cities in northern China lifted stringent capacity restrictions imposed during the five-month winter heating season as part of Beijing's efforts to clear up its notorious foul air.
The official heating season ended on March 15, although major steelmaking hub Handan extended a 50-percent output capacity curb until the end of March.
Output over the first four months of the year was 288.97 million tonnes, up 5 percent on the same period last year, NBS data showed.
Analysts have said that higher output was the main reason behind an increase in steel exports in April, despite hefty tariffs slapped on by the United States and high steel prices .
The record output came even after Beijing phased out 150 million tonnes of excess steel capacity and 120 million tonnes of low-grade steel capacity in the past five years. It plans to shut another 30 million tonnes by the end of this year.
"The market already has a consensus that capacity cutting is not equivalent to output reduction. Production at steel mills is unlikely to fall unless new environmental policy comes out," said Wang Yili, analyst at Sinosteel Futures.
"Downstream demand, especially infrastructure construction, went better than expected this spring. Also, the fat margins encouraged mills to churn out more products."
Profit margins for rebar-making touched 608 yuan ($95.81) a tonne in April, up more than 40 percent from a month earlier, Mysteel data showed, while Jefferies had estimated rebar margins at a 10-year high of $134 per tonne.
Production of coke, used in steelmaking, fell 3.6 percent in April to 36.72 million tonnes compared to the same period last year due to an environmental crackdown across the country. But output in April was the highest since September 2017.
($1 = 6.3457 Chinese yuan renminbi) (Reporting by Muyu Xu and Josephine Mason Editing by Joseph Radford)