COCHABAMBA, Bolivia, Oct 5 (Reuters) - Leftist Bolivian President Evo Morales and a block of opposition governors restarted talks on Sunday to ease political tensions that triggered a wave of protests and deadly clashes last month.

The conflict between Morales, the impoverished country's first Indian leader, and governors demanding more autonomy and opposed to his anti-capitalist and pro-Indian reforms sparked clashes in which at least 19 people were killed, most of them Morales supporters.

The unrest shook four provinces run by rightist politicians where anti-Morales groups raided public buildings, attacked energy facilities and blocked roads.

"We're are betting on being able to guarantee autonomy for all departments and regions ... (but) some governors want autonomy only for some families," Morales told supporters before attending the talks in the central Cochabamba province.

Although Morales has said he hopes for a deal to be signed on Sunday, the pro-autonomy governors have said the meeting would serve only to relaunch the negotiations.

Four governors agreed to meet with Morales in mid-September, but walked out of talks on Wednesday to protest the arrest of a demonstrator the government says led attacks on two natural gas facilities.

A fifth opposition governor was arrested last month accused of being responsible for the deaths of at least 15 Indian peasants in the northern Pando province during the clashes.

The talks hit a snag when the opposition asked for significant changes to a draft constitution approved last year in an elected assembly they had boycotted.

The government refuses to bow to some of the governors' demands because they say they only represent "a minority". There are nine provinces in Bolivia.

According to government officials, substantial progress has been made on the governors' calls for more autonomy and a larger share of the country's booming energy revenues.

Morales says the new constitution is a tool to grant more rights to the long-neglected Indian majority, but the governors want the charter rewritten, saying it would allow the president to amass too much power.

Although Morales won an August recall vote with 67 percent of support, the bulk of the opposition governors also achieved sweeping victories in their constituencies.

Morales' power base is among impoverished Indians in the western highlands but his leftist reforms are unpopular among mixed-raced people in relatively wealthier regions governed by the opposition. (Reporting by Danilo Balderrama in Cochabamba and Carlos Quiroga in La Paz; Writing by Eduardo Garcia; Editing by Kevin Gray)

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