By Tarek Amara

TUNIS (Reuters) - Tunisia's new Islamist-led government won a confidence vote on Wednesday, as the death of an unemployed man who had set himself on fire in despair underscored the scale of its task.

Prime Minister Ali Larayedh has said the government, which was backed by 139 of the National Constituent Assembly's 217 members, would serve only until an election later in the year.

Tunisia, economically struggling and deeply polarized between Islamists and their opponents, is in the throes of a political transition that began with the overthrow of strongman Zine al-Abidine Ben Ali in a popular uprising two years ago.

The revolt was sparked by the death of Mohammed Bouazizi, a street vendor who torched himself on December 17, 2010 after a policewoman seized his fruit cart in the town of Sidi Bouzid.

Adel Kedhri, 27, was the latest of several Tunisians to emulate Bouazizi's fiery protest. A medical source said he had died in hospital after setting himself alight in the center of Tunis, the capital, on Tuesday.

"We received the message," Larayedh said of Khedhri's death on Wednesday, without commenting further.

Presenting his government's program the previous day, he said its priorities would be tackling unemployment, now at 17 percent, and rising prices, along with providing security.

The economic and social problems that fuelled Tunisia's uprising have yet to be solved and often spark unrest. Feuding politicians have missed deadlines to produce a new constitution and set dates for parliamentary and presidential elections.

The malaise worsened when secular politician Chokri Belaid was assassinated in broad daylight on February 6 in what the authorities say was an attack by Salafi Islamist militants

The previous government collapsed after the killing, which touched off days of mass street protests.

The new one, led by the moderate Islamist Ennahda party along with two junior secular coalition partners, resembles its predecessor, although in a concession to its critics Ennahda has ceded control of some key ministries to independents.

The assembly, split over Islam's role in society and over the powers of president and parliament, will vote later today or Thursday on a new timetable for the constitution and elections.

Those polls would end a transitional period in which Tunisia has had four interim governments since Ben Ali's overthrow.

(Reporting by Tarek Amara; Editing by Alistair Lyon)