SINGAPORE, May 13 (Reuters) - Spot differential for Asia 380-cst high sulphur fuel oil (HSFO) was back in a thin premium on Tuesday, while market backwardation widened at the prompt months for all key grades.

The differential was near parity to cargo quotes in the last trading session, having recovered from discounts previously.

Some spot bids for HSFO edged higher this week, though broader trading momentum remained largely quiet.

Refining cracks for the product gained, with the June contracts LFO05SGBRTCMc1 closing near premiums of $3 a barrel, based on LSEG's data.

Meanwhile, very low sulphur fuel oil (VLSFO) market was rangebound amid an absence of fresh drivers, with cracks for VLSFO holding above premiums of $12 a barrel.

REFINERY UPDATES

- Chevron is attempting to restart the El Segundo, California refinery after taking units offline last week, sources familiar with plan operations said.

OTHER NEWS

- Oil prices edged higher on Tuesday, with gains capped by rising supplies and caution over whether the pause in the U.S.-China trade war will lead to a longer-term deal. O/R

- Saudi Arabia's crude oil supply to China is set to hold steady in June, trade sources said on Tuesday.

- Black Sea CPC Blend oil exports via the Caspian Pipeline Consortium system were set at 1.5 million barrels per day (or about 6 million metric tons) for May, down from some 1.6 million barrels per day in April, two industry sources said.

- The container shipping industry welcomed an agreement between the United States and China to temporarily slash punishing tariffs, saying it expected to be buoyed by a resulting recovery in bookings from China to the U.S.

WINDOW TRADES O/AS

- 180-cst HSFO: No trade

- 380-cst HSFO: No trade

- 0.5% VLSFO: No trade

ASSESSMENTS

(Reporting by Jeslyn Lerh; Editing by Shailesh Kuber)

((jeslyn.lerh@thomsonreuters.com))