* Former PM Abhisit wants to broker talks to end crisis
* PM Yingluck could be removed by courts in May
* Economy is suffering: industrial output slumped in March
* March exports fall, imports slump (Adds March trade figures)
By Amy Sawitta Lefevre
BANGKOK, April 28 (Reuters) - Thai opposition leader Abhisit Vejjajiva met the head of the armed forces on Monday to discuss ways to avert a showdown between rival political factions next month that threatens more bloodshed and economic damage.
Former Prime Minister Abhisit, who met Armed Forces Supreme Commander General Thanasak Patimaprakorn, has asked for two weeks to try to resolve the crisis peacefully.
"He supports what I want, which is to bring all sides together to find a way out for the country," Abhisit told reporters after a two-hour meeting with Thanasak.
"The commander underscored that political problems must be solved through political means."
Prime Minister Yingluck Shinawatra has faced months of anti-government protests aimed at removing her and ridding the country of the influence of her brother, former premier Thaksin Shinawatra.
The protests are the latest phase of nearly a decade of confrontation between Thaksin and the Bangkok-based royalist establishment who see Thaksin, a populist former telecoms tycoon, as a threat to their interests.
The protesters accuse Thaksin of corruption and nepotism, which he denies. They want an unelected "people's council" to oversee reforms to tackle graft and end what they see as Thaksin's money politics.
Thaksin, who was ousted in a 2006 military coup and lives in self-imposed exile to avoid a jail sentence for graft handed down in 2008, remains hugely popular among the rural poor in the north and northeast.
The military, which has intervened frequently in politics in the past, has stayed out this time, although its leaders have said they will intervene if violence worsens.
Twenty-five people have been killed in politically related violence since the unrest began in November, most of them in shootings and grenade blasts.
The turmoil has dented business confidence, especially as Yingluck has headed a caretaker government with limited powers since dissolving parliament in December.
Data on Monday showed that industrial output in March was 10.4 percent lower than in March last year.
Later, the Commerce Ministry released data showing exports fell 3.12 percent in March from a year earlier due to a lacklustre global economy, while imports were down 14.19 percent.
The central bank has warned that the economy could contract in the first quarter compared with the final three months of 2013. It has cut its 2014 growth forecast several times and said last week it would probably fall short of its most recent forecast of 2.7 percent.
Yingluck's government triggered the protests late last year by trying to push through an amnesty bill that could have allowed Thaksin to return without facing jail time. The demonstrations quickly turned into a bid to oust Yingluck.
The rallies have waned in recent weeks but that has not deterred protest leader Suthep Thaugsuban, who has promised a "final push" to oust Yingluck in May.
The protesters are also pinning their hopes on legal cases that could lead to Yingluck's removal from office within weeks.
She has been charged with abuse of power for her transfer of National Security Council chief Thawil Pliensri in 2011, which opponents say was done for personal and party political reasons. If found guilty, she may have to step down.
Yingluck has until Friday to present her defence.
She also faces charges of dereliction of duty over a state rice subsidy scheme that has incurred billions of dollars in losses and left hundreds of thousands of farmers unpaid.
But supporters of the Shinawatras have vowed to resist efforts to unseat Yingluck and they plan a big rally on the outskirts of Bangkok on May 6. Both sides can whip up large crowds and both have armed activists in their ranks.
Abhisit, who has taken part in some of anti-government rallies, launched his reconciliation bid saying he wanted to avert more violence.
But his proposal for an election to take place alongside political reforms has met with a lukewarm response from both pro-government leaders and protest leader Suthep.
The cabinet on Monday extended an Internal Security Act in Bangkok and surrounding provinces until June 30. It allows the authorities to impose curfews, operate checkpoints and restrict the movement of protesters.
However, it has done little to curb the protests and the government has been reluctant to use force against protesters for fear of a backlash. (Additional reporting by Aukkarapon Niyomyat and Panarat Thepgumpanat; Editing by Alan Raybould and Robert Birsel)