* Deeper cut possible, no real discussions now-delegate
* OPEC/non-OPEC panel to discuss options at July meeting
* Some delegates cite Libya/Nigeria exemptions as drawback
LONDON, June 27 (Reuters) - OPEC will not rush into making a further cut in oil output or end some countries' exemptions to output limits, OPEC delegates said, although a meeting in Russia next month is likely to consider further steps to support the market.
OPEC and allied non-OPEC producers agreed on May 25 to extend an existing supply cut into 2018, but oil has fallen sharply then on rising production from the United States and from Nigeria and Libya, two OPEC members exempt from cutting output.
"I doubt it will be considered soon," said an OPEC delegate, referring to the chance of a larger cut. "They will look at this issue most probably in the upcoming meeting in Russia in July."
Oil ministers from five countries monitoring the deal plus Saudi Arabia as OPEC president are scheduled to meet in Russia on July 24. They could make a recommendation to the wider group, which holds its next meeting in November, on adjusting the pact.
"A larger cut could be an option," said another OPEC delegate, adding that further steps could be to place caps on further growth in Nigerian and Libyan output, rather than requiring them to cut back their supply.
A third source familiar with the matter agreed that removing more crude from the market was an option but said it was not being actively considered.
"It is possible but there are no real discussions now," this source said, and added that a drawback of the current supply-limiting deal was Nigeria and Libya being exempt.
Comments from key oil ministers also suggest the OPEC-led group is in no rush.
Iran said last week OPEC was considering further cuts but should wait until the effect of the current reduced level of production became clear.
Saudi Energy Minister Khalid al-Falih was quoted on June 19 as saying the market was heading in the right direction, while Russia said on June 11 there was no need to review the deal.
Falih also said it would be "inappropriate" to pressure Libya to slow its output recovery.
The Organization of the Petroleum Exporting Countries, Russia and other producers initially agreed to cut production by 1.8 million bpd for six months starting on Jan. 1.
Nigeria and Libya were exempted from the cut because of production losses caused by unrest. Iran was given a small increase so it could recover market share lost while under Western sanctions.
While the participating countries have delivered high compliance with their cut pledges, OPEC output has been rising led by recovering output in Libya and Nigeria. In May, this tipped the global market back into surplus according to OPEC's monthly report.
Nigeria has said it would be willing to join OPEC cuts if production rose to around 1.8 million barrels per day. The country is nearing that rate and planned exports in August imply production of at least 2 million bpd.
Libya is targeting production of 1 million bpd by the end of July, up from an average of 650,000 bpd in the first quarter.
(Additional reporting by Rania El Gamal; editing by Jane Merriman)