TOKYO/SEOUL (Reuters) - Abu Dhabi National Oil Co. (ADNOC) will maintain crude oil term supply volumes to Asia in June at May levels, lifters said on Tuesday, in line with OPEC's decision last month to keep existing supply curbs.

The main producer in OPEC-member United Arab Emirates (UAE) has told at least two refiners, one Japanese and one South Korean, that it would keep its crude supplies at steady levels.

Traders said the move was expected and two lifters said they did not seek additional supplies on top of their contracted volumes.

Term crude sales to Asian refiners have not been curbed since they were restored to full volume from March supplies.

"There was no cut for the term volumes for June," one lifter said.

The UAE is the first OPEC producer to notify customers of June supplies.

Two separate Japanese lifters said they had not yet received notice from ADNOC, which produces just over half of the UAE's oil, most of which is shipped to Asia.

OPEC President Mohammed al-Hamli said last week that global oil markets were well-supplied but the group stood ready to increase output if needed.

Now that ADNOC's supply plans are out, focus would shift to top oil exporter Saudi Arabia, which is set to inform its customers about June supplies in the next few weeks.

State oil firm Saudi Aramco earlier this month notified its Asian customers that it would keep supply curbs steady for May as in April at 9-10 percent below contracted volumes.

In late December, ADNOC said it would cut some crude supplies in February by 3-5 percent, versus full contracted volumes in January, after the Organization of the Petroleum Exporting Countries decided to cut output by 500,000 barrels per day (bpd) from February.

The output cut came on top of the previously agreed 1.2 million-bpd reduction made from Nov. 1, as OPEC moved to halt a 25 percent slump in oil prices to below $60 a barrel.

OPEC decided in mid-March to keep its exports curbs totaling 1.7 million bpd.

Abu Dhabi crude accounts for most oil exports from the UAE, which has agreed to cut output by 143,000 bpd from Feb. 1 out of total production of around 2.5 million bpd.

U.S. crude futures fell by 17 cents to $65.72 a barrel on Tuesday after the previous session's $1.78 jump, as traders worried about supply disruptions from Nigeria.