* Run-off vote is fourth attempt to choose leader

* Role of Islam in Maldives central to campaigns

* Tourism in island paradise has been hit (Adds voting, quotes, colour)

By J.J. Robinson

MALE, Nov 16 (Reuters) - Voters in the Maldives thronged to polling stations on Saturday to choose a new president, hopeful that the run-off election resolves a two-year political crisis which has hit the vital tourism sector in the island paradise.

Three previous attempts to elect a new leader have been annulled or postponed in as many months, as narrow election favourite Mohamed Nasheed and the parliament have clashed with a political old guard backed by the Supreme Court.

Tattered pink and yellow party banners were suspended above the capital Male's narrow streets, providing shade from the hot tropical sun.

Voters queuing up outside the Kalaafaanu School voiced unease about the outcome of the ballot, after an aggressive campaign by the two candidates contesting the second round and following sporadic violent protests in recent months.

"Today is absolutely critical for democracy and the future of our country," said 48-year-old Fareesha Abdulla. "It will determine whether we become a democracy or a dictatorship."

Nasheed, who became the Maldives' first democratically elected president in 2008, left office last year in what he says was a coup. He won 47 percent of first round votes a week ago, short of the 50 percent needed to avoid a run-off.

He is up against Abdulla Yameen, a half-brother of Maumoon Abdul Gayoom, who ruled for 30 years and is considered a dictator by opponents and rights groups.

Polls close at 4 p.m. (1100 GMT) and Election Commissioner Fuwad Thowfeek told state television that the final results would be announced early on Sunday.

"NOT MUCH I CAN DO"

The term of the incumbent president, Mohamed Waheed, expired on Nov. 11, but when the Supreme Court delayed the second round of voting following demands by Nasheed's rivals, Waheed extended his term to fill a constitutional void.

Waheed, whose decision drew international condemnation, left for Singapore on Friday, saying: "I do not think there is much I can do from here, things that I cannot do over the phone."

The Maldives' political upheaval has hit tourism, a vital source of foreign currency, resulting in the idyllic Indian Ocean archipelago being unable to import all of its fuel needs.

Political analysts say the crisis may continue even if Saturday's vote goes smoothly, after a bitter election campaign centring on the future role of religion in a largely Muslim state where Islamist ideology is on the rise.