* PM promises resignation but has yet to quit
* Parliament to resume Tuesday, opposition says has majority
* Analysts say uncertainty will delay LNG developments (Writes through with comment from politicians, analyst, updates shares)
By Tom Westbrook and Sonali Paul
SYDNEY/MELBOURNE, May 27 (Reuters) - Political turmoil in Papua New Guinea deepened on Monday as the opposition raised doubts about an offer from Prime Minister Peter O'Neill to resign and vowed a long fight to get rid of him as uncertainty knocked shares linked to its resources sector.
Instability is not unusual in the South Pacific archipelago and it has not held back mining and energy investment in the resource-rich but poverty-stricken country.
However, protests over the benefits of investment failing to reach the hinterland have dogged the government, sapping enough support from the ruling coalition for the opposition to claim it can now command a parliamentary majority.
O'Neill had resisted calls to resign for weeks but his opponents said on Friday they had rallied enough support in parliament to oust him.
He said on Sunday he would quit in favour of Sir Julius Chan, a two-time former premier.
But O'Neill has yet to formally resign, and has said he has filed a court challenge to a looming vote-of-no-confidence. At the same time, it is not clear if an opposition-dominated chamber would accept Chan when parliament resumes on Tuesday.
O'Neill's spokesman said on Monday he would not quit before his court challenge to the procedure for a no-confidence vote is heard, and there is no timetable for that.
William Duma, who quit his position as state investment minister on Friday and led his party over to the opposition, said O'Neill was key to ending the political crisis.
"If he does the honourable thing and resigns it'll be over and we will have a new leader," Duma said by telephone from the Lagnua Hotel in the capital, Port Moresby, where the opposition has been camped for weeks mustering support.
"If he drags it, we are prepared to go in for the long haul because we have lost our respect for him," he said, citing corruption accusations - which O'Neill denies - and what he described as the prime minister's dictatorial style among reasons for his defection from the government's ranks.
Analysts say political turbulence will delay projects on the drawing board and put future plans under a cloud, and oil majors with interests in PNG, Total SA TOTF.PA and ExxonMobil Corp XOM.N , will be watching closely.
Paul Barker, executive director at Port Moresby-based think-tank Institute of National Affairs, O'Neill could be playing for time, perhaps in the hope of building new alliances.
"A lot of people think that it's a fudging exercise to draw the process out for a fair while and to somehow avoid the vote of no confidence," Barker said.
"PNG politics is a very fluid thing and there are not many ideological reasons why you would be on one side or another, so you can flow fairly readily."
DEVELOPMENT DELAYS
The impasse threatens to delay a $13 billion plan led by Total to double gas exports, sending shares in one of its partners, Oil Search Ltd OSH.AX , down nearly 4% on Monday.
"The resignation of Peter O'Neill will delay first gas from the LNG expansion projects until beyond 2025," Wood Mackenzie analyst David Low said by email.
"While we still expect the project to go ahead, the political turmoil opens the door to competing projects and increases the risk of knock-on delays."
Chan's position as caretaker is also unclear, after he said he was not seeking the leadership and would only take it if he had the support both government and opposition, which he has yet to secure.
"We will not choose him," opposition lawmaker Allan Bird told Reuters in a text message. "We want a complete break from O'Neill (and) Chan is just a proxy for O'Neill."
If O'Neill is replaced, foreign energy companies could find themselves dealing with a less friendly government.
O'Neill's deal with Total, agreed in April, set the terms for developing the Elk and Antelope gas fields, which will feed two new liquefied natural gas (LNG) production units at the PNG LNG plant, run by ExxonMobil Corp XOM.N . the same time, ExxonMobil and its partners are planning to build a third unit at the PNG plant, to be partly fed by another new gas field, P'nyang.
Credit Suisse (SIX:CSGN) analyst Saul Kavonic said the turmoil could put pressure on the government to negotiate tough terms for the P'nyang gas agreement, which has yet to be finalised, and affect talks on development costs.
"Both these factors heighten the risk of delay," he said in a note to clients.
The uncertainty sent shares in Oil Search, a partner in PNG LNG and Papua LNG, down as much as 4% before they recovered to close almost 2% lower. Energy stocks .AXEJ were flat.
ExxonMobil and its partners had hoped to begin basic engineering planning for the expansion by mid-2019 and make a final investment decision in 2020.
Total and Oil Search representatives were not immediately available to comment.