* Independence, Progressive parties win 19 seats each
* Ruling Social Democrats take distant third
* Voters reject bailout terms and EU membership talks
* Campaign focused on household debt relief
By Balazs Koranyi and Robert Robertson
REYKJAVIK, April 28 (Reuters) - Iceland's centre-right parties began talks on Sunday to form a new government, promising to end years of austerity and provide debt relief to households, and only arguing about which one of them should lead the government.
Fed up with years of belt tightening and soaring debt, Icelanders ousted the Social Democrats on Saturday, handing the biggest defeat to any ruling party since independence from Denmark in 1944 and offering a new chance to the very parties that presided over its economic rise and collapse.
"The best solution would be a two-party coalition; that would be the strongest type of government capable to handling the tough decisions ahead," Independence Party leader Bjarni Benediktsson, 43, said on Sunday, calling a coalition of the two centre-right parties a "natural first choice".
With all the ballots counted, the Independence Party, which took part in every government between 1980 and 2009, won 26.7 percent of the vote and 19 seats in the Althing, the world's oldest parliamentary institution.
The Progressive Party, its main rival and partner in many previous coalitions, scored 24.4 percent, also worth 19 seats, while the Social Democrats were a distant third with 12.9 percent.
"Independence Party and Progressive Party teaming up in a coalition is by far the most likely outcome. Other outcomes are of course possible but very unlikely," Olafur Hardarson, a political science professor at the University of Iceland said on Sunday, when the final votes came in.
In a country where Nordic civility prevails, the prime minister walks without security and members of parliament are listed in the phone book. Coalitions are usually formed in just days and experts said it would be a quick deal once again.
President Olafur Ragnar Grimsson said he would decide by Monday evening who he would ask to form the government.
Progressive Party leader Sigmundur Gunnlaugsson, 38, argued that he should lead the government because his party made the biggest gains, more than doubling its seat in parliament.
"I would think we are in a position to be offered to lead the government. We have gained most support," he said.
Once a European financial centre, the windswept north Atlantic island of glaciers, geysers and volcanoes has struggled along for years after a crash that brought it to its knees.
"A lot of people are struggling and they are expecting a lot from this next government, maybe even magic," Reykjavik voter Haraldur Johannsson, 57, said. "All the parties make promises but they often don't keep them so perhaps we should be careful in what we wish for."
The two parties campaigned on offering households debt relief as falling property prices and inflation-indexed mortgages keep pushing debt higher, despite several rounds of write-offs.
They also argued that foreign investors, primarily hedge funds, who hold claims to the collapsed banks, must take a huge write-off, possibly as much as 75 percent, before capital controls can be lifted. And both argued that Iceland should end talks to join the European Union, preserving independence.
"People seem to have a very short memory," Halldor Gudmundsson, 44, said after casting his ballot on Reykjavik's outskirts. "These are the parties that got us into the mess in the first place."
The two parties presided over Iceland for years, setting in motion its unchecked economic liberalisation, which led to a phenomenal rise and crash.
Iceland's privatised banks borrowed on cheap overseas markets and lured British and Dutch savers with high returns.
But after amassing assets worth more than 10 times Iceland's GDP, Landsbanki, Kaupthing and Glitnir collapsed in quick succession, dragging the entire country into a financial abyss in October 2008.
Property prices tumbled, unemployment soared and the currency was only saved by capital controls that locked in foreign investors indefinitely.
The Social Democrats stabilised the economy with a bailout package hailed as exemplary by the IMF. But a series of policy blunders, tax hikes, leniency toward foreign creditors and their inability to deal with household debt cost them popularity.