By Mirwais Harooni

KABUL (Reuters) - Thousands of people from Afghanistan's Hazara minority demonstrated in the capital Kabul on Saturday to demand changes to the route of a planned multi-million dollar power transmission line.

The demonstrators are demanding the 500 kV transmission line from Turkmenistan to Kabul be rerouted through two provinces with large Hazara populations, an option the government says would cost millions and delay the badly needed project by years.

Waving Afghan flags and chanting slogans like "Justice!" and "Death to discrimination!", demonstrators gathered near Kabul University, several kilometers from the main government area.

Much of the city center was sealed off with stacks of shipping containers and other obstacles and security was tight with helicopters patrolling overhead but there was no violence.

"The people you see haven't come only to leave empty-handed," said Mohammad Hussain Ahmadi, 33. "The government has to change the route or protests will continue for weeks."

The transmission line, intended to provide secure electricity to 10 provinces is part of the so-called TUTAP project backed by the Asia Development Bank, linking energy-rich states of Central Asia with Afghanistan and Pakistan.

Hazaras say they want the line to come through Bamyan and Wardak provinces, west of Kabul, where many Hazaras live, to ensure their power supply.

The government says the project already guarantees ample power to the two provinces and denies it disadvantages Hazara people, a mainly Shia minority.

Under current plans, due to be implemented by 2018, the line will pass from a converter station in the northern town of Pul-e Khumri to Kabul through the mountainous Salang pass.

An earlier plan foresaw a longer route from Pul-e Khumri through Bamyan and Wardak, but this option was dropped.

The Persian-speaking Hazara, estimated to make up about 9 percent of the population, are Afghanistan's third largest minority but they have long suffered discrimination. Thousands were killed during Taliban rule.

However, they are politically well organized and several of their leaders are in President Ashraf Ghani's delicately balanced national unity government, which has added to the sensitivity surrounding the demonstration.

The protests also risk exacerbating tensions with other ethnic groups and provinces that the government says would have to wait up to three years for power if the route were changed.

Saturday's demonstration follows a protest in May, after which Ghani promised a committee of inquiry. That committee however recommended keeping the Salang pass route.

Upgrading Afghanistan's creaking power network is among the government's top priorities as currently only 30 percent of the country is connected to the electricity system.

(Writing by James Mackenzie; Editing by Robert Birsel and Tom Hogue)