(For the 12-month forward curve, click ) SINGAPORE, July 1 (Reuters) - The Asian fuel oil market rebounded on Friday after easing for the past two sessions, with prompt cracks and fixed-price levels strengthening despite lower crude benchmarks, while prompt cash premiums for the 380 centistoke (cst) grade jumped to a month high above $7 a tonne. Oil major BP emerged as the buyer of all four of the day's cargoes after a lull of more than three weeks in the physical market, while Brightoil was on the opposite side, selling two of the cargoes and also was the day's biggest seller in the swaps market, accounting for 135,000 tonnes of the day's 170,000 tonnes of visible July volumes. BP's strong buying in the 380 cst market, which lifted the grade's cash differential by nearly 25 percent, also narrowed the physical viscosity spread to about $6 a tonne, its lowest level in five months, Reuters data showed. "It's the start of a new calendar month, and the pricing interests are back in the market after a lull of nearly a month. And it would seem that it's BP and Brightoil yet again, but on opposite sides to where they were in May," said a Singapore-based Asian fuel oil trader. "It would appear that BP's activities are driven by the viscosity spread, which has been narrowing for over a week now, while Brightoil's look like a straightforward bear timespread play, but it's too early to tell." The front-month July viscosity spread has fallen to five-month low levels of around $9.25 a tonne since the end of last week from $12 around two weeks ago, fundamentally driven by record-high arrivals from Iran, totalling 1.2 million tonnes, of mostly on-specification 380 cst cargoes. Traders also point out that BP has been buying relatively large volumes of July- and August-lifting cargoes via spot tenders, including 250,000-300,000 tonnes of high 700 cst viscosity cargoes from Yanbu, about 160,000 tonnes of 380-cst from Mangalore and at least 45,000 tonnes of 180 cst from Haldia in each loading month. The narrowing viscosity spread could be related to their pricing activities surrounding these purchases, they added. Fundamentally, the market is expected to be stronger this month, versus June, largely due to lower Iranian volumes, notionally estimated at 750,000-800,000 tonnes, while Western supplies remain at below-average levels of under 3 million tonnes for a second straight month. In contrast, demand remained stronger-than-normal, from unexpected sources, such as Bangladesh and Malaysia, although prompt ex-wharf bunker demand has been dampened by rising crude benchmarks, with its premiums to cargo levels falling for a third straight session to below $8.00 a tonne. Brent crude's August contract LCOc1 was at $110.76 a barrel by the Asian close, down 77 cents and falling for the first time in four sessions. * SWAPS SPREADS: July/August eased for a second session to a backwardation of $4.75 a tonne, down 50 cents, by the Asian close at 0830 GMT, with 30,000 tonnes traded at $4.75-$5.00, down from 130,000 tonnes, and last offered lower at $4.50 after the close by 1130 GMT. August/September was higher at $4.00 a tonne, up 13 cents, with 80,000 tonnes traded at $3.75-$4.00, another 20,000 tonnes of September/October at $2.00-$2.25, 20,000 tonnes of October/November at $2.00 and 15,000 tonnes of November/December at $1.50-$1.75. Activity in the quarterly spreads eased, with only 30,000 tonnes of Q4/Q1 traded at $2.75-$2.95 a tonne, while 25,000 tonnes of the July viscosity spread traded at $8.00-$8.25. * SWAPS OUTRIGHTS: The July and August 180 cst swaps were valued at $653.00 and $648.25 a tonne, up $1.38-$1.88, or 0.2-0.3 percent, with 175,000 tonnes of July traded at $653.00-$654.00, up from 120,000 tonnes, after the close. Another 20,000 tonnes of August were transacted at $648.00-$648.25, and last offered at $649.50, while another 40,000 tonnes of July 380 cst were traded at $644.25-$645.00 a tonne. * EAST-WEST SPREADS: EAST-WEST SPREADS: The East-West spreads narrowed for a second session, with July and August valued at $34.50 and $35.25 a tonne respectively, down $1.75 and $1.00, for both, with 15,000 tonnes of Q1 traded at $35.25. * SWAPS CRACKS: The August crack strengthened for a second session, up jumping by 90 cents to a discount of $5.83 a barrel to Dubai crude, while its September contract gained 92 cents to a discount of $6.68. * CARGO PRICES AND DIFFERENTIALS: The 180 cst grade rose for a fourth session to $656.15 a tonne, up $1.20, while the 380 cst grade gained $3.75 to $650.15. The differential for the 180 cst grade slipped to $4.38, down a slender 13 cents and falling for a third session, but that for the 380 cst grade jumped a massive $1.38 to $7.13. * TENDERS: Thailand's PTT bought 20,000 tonnes of 0.5 percent sulphur fuel oil, for prompt July 7-15 delivery to Map Ta Phut, from Vitol at a premium of $160.00-$170.00 a tonne to Singapore spot quotes, on a cost-and-freight (C&F) basis, the highest for the 0.5 percent sulphur grade in over a year. It is also seeking another 30,000 tonne lot, for July 7-26 delivery, C&F, with a deal expected by next week. * CASH DEALS: Four deals -- Brightoil sold two 180 cst cargoes of 21,000 tonnes each, for loading July 16-20 and July 26-30, to BP at respective premiums of $3.00 and $1.50 a tonne to average first-half July quotes, equivalent to premiums of $4.60 and $4.81 to Singapore spot quotes. The oil major also bought two 380 cst parcels of 38,000 tonnes each, both for July 16-20 lifting, from Chevron and Kuo Oil at premiums of $4.50 a tonne to spot 380 cst quotes.

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