The protester died of wounds suffered when he was run over by a national guard vehicle during clashes with security forces.
Anouar Sakrafi, in his early 20s, died of wounds suffered Monday when he was run over by a national guard vehicle during clashes with security forces at an oil and gas plant, the scene of long-running protests over joblessness.
Security forces fired tear gas as protesters tried to storm the El Kamour facility in the desert region of Tataouine, radio reports said.
The government said Sakrafi's killing was accidental.
A stream of vehicles was seen heading for his burial in his home town of Bir Lahmer, 30 kilometres (20 miles) from the city of Tataouine.
"With our souls, with our blood, we sacrifice ourselves for you, martyr!" thousands of mourners chanted before the funeral, which passed off peacefully.
Protesters have been camped outside the El Kamour pumping plant for about a month, blocking trucks from entering, to demand a share of resources and employment in the sector.
Calm prevailed at the plant on Tuesday.
In the city of Tataouine, also the scene of Monday's clashes, stones and tyres littered the streets and buildings showed evidence of having been set alight.
Most shops were closed and police stations were deserted.
Behi Labia of the Tataouine court said an investigation had been launched over "damage to public property".
Sofiane Nasri, 25, a member of the organisation committee for the El-Kamour sit-in, told AFP his movement had nothing to do with the damage.
He accused other parties of wanting to "harm the movement" or "settle scores".
Six years since the uprising that toppled veteran dictator Zine El Abidine Ben Ali, Tunisia is facing renewed protests over joblessness and perceived marginalisation of the country's periphery.
National guard spokesman Khalifa Chibani warned Tuesday of further escalation.
"There is incitement on social media... calls for civil disobedience... and even a coup d'etat," he told Mosaique FM radio station.
In a special sitting of Tunisia's parliament, assembly president Mohamed Ennaceur said Tunisia was "passing through a delicate phase".
Tataouine residents have long demanded more jobs and a bigger share of the revenues from oil extraction in the region.
Last month protestors there booed Prime Minister Youssef Chahed off stage during a heated town hall meeting.
On Monday the health ministry said 50 people were hospitalised with broken bones or the effects of tear gas during the clashes in both El Kamour and Tataouine.
Authorities said about 20 members of the security forces were injured.
Two protests were held in the capital, with demonstrators echoing the rallying cry of Tataouine residents and chanting: "We won't give up!"
Mosaique FM said fighting also broke out overnight during a rally in Kebili, 230 kilometres (140 miles) northwest of Tataouine, in support of the El Kamour protesters.
A hundred or so people also demonstrated on Tuesday morning in the central town of Gafsa, an AFP reporter said.
President Beji Caid Essebsi vowed this month to deploy the army to protect key economic installations from disruption by protests.
But a group set up to coordinate protests across Tunisia blamed Essebsi for Sakrafi's killing.
"The head of state is responsible for this death, for what happened in Tataouine and in other regions, especially after his speech" on deploying the army, said the National Coordination of Social Movements.
The unrest comes as parliament debates a disputed bill that would allow officials facing prosecution for alleged corruption to be amnestied in exchange for paying back embezzled funds.
The bill, backed by Essebsi, has prompted a backlash from civil society groups which say it would "whitewash the corrupt".
Government spokesman Iyed Dahmani insisted Tunisia had a "democratic regime".
"In all democracies, there is no other solution: apply the law and dialogue with the protesters," he told Shems FM radio.
But La Presse newspaper warned "the anger of the protesters (could) snowball".
It said the government must tackle the issue, which "makes Tunisians feel that nothing has changed since January 14, 2011" -- the day Ben Ali fled the country he had dominated for more than two decades.
"Otherwise, the worst is to be feared."