UPDATE 1-Greenland's ruling party to seek coalition after narrow election win

* Main opposition party not far behind in vote

* Government must deal with shrinking economy, investors

* Country has some of world's largest mineral deposits (Adds analyst comment, background on mining)

By Sabina Zawadzki

COPENHAGEN, Nov 29 (Reuters) - Greenland's ruling SiumutParty narrowly won a snap election, results showed on Saturday,but its new leader Kim Kielsen will need to build a coalition toform a government to deal with a shrinking economy and reassureforeign investors.

The fall of premier Aleqa Hammond last month in an expensesscandal has muted a nationalist rhetoric that promisedindependence from Denmark based on wealth from some of thelargest mineral deposits on earth.

With nascent mining projects languishing due to persistentlylow commodity prices and regulatory uncertainty, analystsexpected any victor in the polls to focus on reviving asubsidised economy heading for its third year of recession.

Siumut, which has formed every single government inGreenland but one since 1979, won 34.3 percent of the vote.Opposition party Inuit Ataqatigiit, led by Sara Olsvig, won 33.2percent, Greenland's official election website showed.

Although both parties won the same amount of seats inparliament - 11 each out of a total of 31 - Kielsen is expectedto lead coalition negotiations as his party received more votes.

Greenland, whose capital Nuuk is closer to New York thanCopenhagen, became a Danish colony in the early 19th century buthas been gaining its own powers since World War Two, introducinga parliament in 1979 and self-governance in 2009.

Just 56,000 people live dotted around the coast of thelargest non-continental island on earth.

A Siumut-led government may comfort the few foreigninvestors who have ventured into Greenland to develop mining. Agovernment led by the party lifted a ban on uranium mining lastyear, opening the door to rare earth projects which oftengenerate uranium as a byproduct.

So far companies from Australia and Canada have enteredGreenland to mine a variety of minerals, some with Chinesecontractors.

Inuit Ataqatigiit had vehemently opposed the lifting of theban and had promised to reinstate it, although the party waskeen to emphasise it was not against mining per se.

"Overall, the outcome of this election is very good news forinvestors, especially in the mining and infrastructure sectors,"said Mikaa Mered, analyst and managing partner at consultancyPolarisk.

"With Siumut remaining in power ... we expect Greenland tostabilise itself - both from a political risk and a regulatoryrisk standpoint - whilst keeping the country's march towardsindependence."

There are about 40,000 eligible voters in Greenland, 29,500of whom voted - marking a turnout of above 70 percent. (Editing by Pravin Char)