* Thousands attend funeral of slain politician
* Parliament may reach new power sharing deal-spokesman
* Salafist group denials role in assassination (Recasts with Sidi Bouzid clashes, updates parliament talks)
By Tarek Amara
TUNIS, July 27 (Reuters) - Tunisian police fired teargas late on Saturday to disperse violent protests in the southern town of Sidi Bouzid, cradle of the country's revolution and hometown of slain secular opposition figure Mohamed Brahmi, witnesses said.
Tensions have run high in Tunisia since Brahmi's Thursday assassination, and large protests throughout the day were met with police teargas.
In a bid to stave off unrest amid intensifying protests, particularly in the capital, secular coalition partners of Tunisia's ruling Islamist party said they were in talks to reach a new power-sharing deal.
The spokesman for the Constituent Assembly, Tunisia's transitional parliament tasked with drafting a new constitution for the North African country of 11 million people, said he expected a deal in the coming hours.
"The trend now is to move towards expanding the base of power," Mufdi al-Masady told a local radio station.
The effort to reach a new deal by secular coalition partners of the ruling Ennahda party could help defuse increasingly hardline rhetoric on both sides. But so far, protests in the country have continued.
In Sidi Bouzid, locals told Reuters that angry protesters threw rocks at police.
"Hundreds of protesters lit tyres on fire to block roads and they threw rocks at the police," resident Mahdi al-Horshani told Reuters by telephone. "There is a lot of anger and frustration at the situation."
Tensions have skyrocketed in Tunisia since Brahmi's killing, which came just months after another secular opposition figure was gunned down. Secular opposition groups immediately began organising protests and demanded the dissolution of the Islamist-led government.
Their efforts have been fuelled by the recent protests and unrest in Egypt, which toppled that country's democratically elected but unpopular Islamist leader a year after he came to power.
The Islamist and secular movements also appeared on the brink of confrontation on Saturday night.
Thousands of secular protesters faced off with hundreds of Islamists defending the legitimacy of Islamist rule on Saturday night, in one of the biggest sets of rival rallies to hit the Tunisian capital in months.
No clashes were reported, but hundreds of police were standing on the sidelines.
Earlier on Saturday, police fired teargas to disperse secular protesters who gathered in front of parliament following the Brahmi's funeral.
Secular opposition parties are demanding the dissolution of the Islamist-dominated government and parliament, known as the Constituent Assembly.
Opposition protesters carried signs saying: "Leave" and "We won't leave before you do."
At a mosque next to the secular opposition rally, Islamist protesters came out in the hundreds, vowing to support the government.
'DON'T THROW IN THE TOWEL'
The speaker of the Constituent Assembly urged lawmakers who had withdrawn from the assembly in protest to return to work at this critical juncture for completing the constitution. By Saturday, at least 52 had withdrawn from the 217-member body.
"I call on them to back down from their decision. It's not rational to throw in the towel just metres away from the finish line," Mustafa Ben Jaafar said in a televised speech.
"The constitution will be agreed on in August and the assembly will finish its work on October 23."
The death of secular opposition figure Brahmi, shot dead, came months after another secular leader, Chokri Belaid, was killed in a similar attack that stoked violent protests.
Brahmi's killing has intensified the divisions between Islamists and their secular opponents that emerged after President Zine al-Abidine Ben Ali was toppled in 2011, sparking a wave of revolutions that felled leaders in Egypt, Libya and Yemen.
Witnesses said one man was killed early on Saturday in an anti-government protest in the southern city of Gafsa. Violence also broke out in several other cities.
A bomb in a police car exploded in Tunis but caused no casualties, as authorities keen to maintain stability cast a nervous eye at events in Egypt where violence has spiralled since the Islamist president was ousted by the military on July 3.
SALAFIST GROUP DENIES ROLE
Khamis Kssila of the opposition Nida Touns party said earlier that departing parliamentarians would begin a sit-in to demand the dissolution of the assembly and formation of a national salvation government - ideas rejected by Prime Minister Ali Larayedh.
Interior Minister Lotfi Ben Jeddou drew a direct link between the latest killing and the assassination of the Popular Front's leader, Belaid.
Aiming suspicion at a hardline Islamist, the minister said the same gun had been used in Thursday's killing as in the Belaid attack.
Authorities have identified 14 Salafists suspected of involvement in Belaid's assassination, and most were believed to be members of the local hardline Islamist group Ansar al-Sharia, he said.
The group denied any role in a statement on Saturday.
"Ansar al-Sharia has no links to this political assassination that was done as part of a known effort whose goal is to drag the country into chaos," it said.
Tunisia's political transition since the revolt that toppled Ben Ali has been relatively peaceful, with the moderate Islamist Ennahda party sharing power with smaller secular parties.
But the government has struggled to revive the economy and has come under fire from secularists who accuse it of failing to curb the activities of Salafi Islamists. (Additional reporting by Fatma Matoussi; Editing by David Evans, Sonya Hepinstall and Peter Cooney)