* Demonstrations against economic conditions and president
* Government offers constitutional reforms
* Opposition says proposals do not go far enough
(Adds father's comment saying son accidentally caught fire)
By Mohammed Ghobari and Mohamed Sudam
SANAA/ADEN, Jan 20 (Reuters) - Thousands protested in southern Yemen on Thursday to reject political reforms proposed by the government, including a limit on presidential terms, saying they did not go far enough.
The government announced its reform plans in the face of growing discontent that sparked sporadic protests this week.
Opposition parties said they would meet on Saturday to discuss the offer, as thousands of people demonstrated in the southern town of Taiz.
President Ali Abdullah Saleh has ruled Yemen for over three decades.
"We want constitutional amendments but we want amendments that don't lead to the continuance of the ruler and the inheritance of power to his children," said Mohammed al-Sabry, head of the opposition coalition and the Islamist party Islah.
"We won't permit these corrupt leaders to stay in power and we are ready to sleep in the streets for our country's sake, in order to liberate it from the hands of the corrupt," Sabry said.
The protests come as Tunisia grapples with fallout from the overthrow of its long-time president Zine al-Abidine Ben Ali, who fled the country after weeks of violent unrest driven by social grievances.
Among the steps put forward by Saleh's ruling party, the General People's Congress, are amendments to guarantee presidential term limits of two seven- or five-year terms as well as voter registration for all Yemeni adults.
The opposition and protesters in Taiz said the reforms did not ensure that Saleh could not run again.
Protests in the south, where many cities are hotbeds of separatist sentiment, have been larger and more widespread than in the north. Several protests over unemployment and economic conditions took place in the southern port of Aden on Wednesday and demonstrators clashed with police.
Yemenis in the north said dwindling protest turnouts in the capital Sanaa meant widespread revolt was unlikely. Analyst Abdulkarim Salam in Sanaa said the tribal systems that dominate Yemeni life were the biggest impediment.
"Of course it's hard to know what will happen in the coming days, but the situation here is different because allegiances here lie first with tribes, clans or even families, " he said.
Yemen, the Arab world's poorest country, is facing soaring unemployment and the oil reserves that buoy its economy are dwindling. Almost half of its population of 23 million lives on $2 a day or less.
Two protests this week at Sanaa University criticised autocratic Arab leaders, including Saleh. Protesters held signs with the warning: "Leave before you are forced to leave."
The pan-Arab newspaper Asharq al-Awsat reported that an unemployed Yemeni youth set himself on fire in the southern province of Baidah on Wednesday, following the example of the young vegetable seller whose self-immolation inspired revolt in Tunisia and copycat acts in Egypt, Algeria and Mauritania.
The young man's father told state television that his son accidentally burned himself when their house caught fire, though some speculated the statement was made under pressure.
Yemen's government is also struggling to quell a resurgent wing of al Qaeda based in the country and cement a fragile truce with Shi'ite rebels in the north.
North and South Yemen united in 1990 under Saleh but the merger lead to a brief civil war in 1994. Many in the south, home to most of Yemen's oil wealth, say the state discriminates against them while exploiting their resources. (Additional reporting by Mohammed Mukhashef; writing by Erika Solomon; editing by Andrew Roche)