* Pinera to offer 3.3 pct LAN stake in market
* Chile's Bethia group to buy remaining 8 pct stake
* Market sees no major changes to airline after sale (Updates with Cueto family holding in loan ahead of sale in paragraph 5-6)
By Juan Jose Lagorio
SANTIAGO, March 24 (Reuters) - Chilean President Sebastian Pinera agreed to sell his remaining stake in airline LAN LAN.SN (LFL.N), worth around $621 million, in the market and to Chile's Bethia group, as he moves to counter growing criticism over a possible conflict of interests.
Pinera, a center-right businessman, had promised to unwind his majority stake in the regional airline before his swearing in earlier this month. A Feb. 27 earthquake delayed negotiations, sources said, pushing back the sale and triggering much criticism from the opposition and even some allies in Congress.
Pinera's holding company, Axxion SA AXX.SN, said in a regulatory statement it will on Thursday auction a block of 11.31 million LAN shares in the market for a starting price of 9,099.58 pesos per share, equivalent to 3 percent of LAN.
With Chile's peso closing at 533.20/533.50 pesos per dollar on Wednesday, the starting price is around $193 million.
The holding company of the Cueto family, now the majority stakeholders in LAN, said on Wednesday evening it had extended a $225 million short-term loan to its own investment arm on the eve of the auction of the 3 percent LAN stake.
The Cueto family's holding company, Costa Verde Aeronautica, did not say what the 5-day loan was for.
Pinera's holding company, Santa Cecilia, has agreed to sell its 99.84 percent stake in Axxion, which holds a further 8.3 percent stake in LAN, to the Chilean group Bethia SA, which holds investments in top retailer Falabella FAL.SN.
Axxion holds Pinera's stake in LAN, which means its sale will effectively unwind his participation in the carrier.
Shares of Axxion fell 4.41 percent to 18 pesos on Wednesday. Axxion and LAN shares were temporarily suspended in the morning by the local bourse as it waited for Axxion to file a regulatory statement over the sale.
Celfin Capital, the investment bank Pinera had hired to carry out his LAN stake sale, said the public offering plus the Axxion deal would finalize the LAN stake sale.
Analysts say they expect few changes to one of Latin America's biggest airlines following the sale.
"Bethia is likely to be a shareholder that will not get involved in the company's operations, but it will be more of a passive shareholder," said Cristina Acle at CorpResearch.
"That means that LAN will continue to be controlled by the Cuetos."
The Bethia group holds investments in businesses that range from agriculture to retail and food products.
"They were not particularly in the sector or were related to the airspace industry," said Claudio Gonzalez, head of research at Tanner brokerage. "In that sense (the sale) was a surprise."
Local media said foreign investors were interested in buying Pinera's remaining shares in LAN.
LAN Vice-President Enrique Cueto said the entry of the Bethia group "means no changes for the airline."
Pinera, who started to divest his LAN stake worth around $1.5 billion in February, had been under growing pressure to finish the sale.
His government has to face a multibillion dollar reconstruction in the wake of the one of the strongest earthquakes ever recorded. The 8.8-magnitude quake and ensuing tsunamis killed hundreds and demolished towns and roads in central-south Chile.
He would need support in a divided Congress to speed up rebuilding, which is seen as crucial for his new government after 20 years of center-left rule.
LAN, which is considered one of Latin America's most profitable airlines, signed a contract in December to buy 30 new Airbus A320 short-haul aircraft worth around $1.97 billion as part of a program to renew its fleet.
The company's net profits tumbled 31 percent in 2009 to $231.1 million amid the worst of the global financial crisis, but saw profits increase in the fourth quarter in what experts say is a sign of recovery in the airline industry.
Shares of LAN rose 0.41 percent to 9,255 pesos. ($1= 533 Chilean pesos) (Additional reporting by Antonio de la Jara and Alvaro Tapia; Editing by Simon Gardner and Richard Chang)