* BBVA 2013 profit up 33 pct to 2.2 bln euros
* BBVA Q4 loss 849 mln eur after Chinese stake sale
* Caixabank, Popular also report rising profit
* But underlying business remains weak (Repeats with link to Breakingviews column)
By Sarah White and Andrés González
MADRID/BARCELONA, Jan 31 (Reuters) - Spain's second-largest bank BBVA and two smaller peers reported a jump in annual net profit on Friday as charges on their soured property loans fell, pointing to a tentative recovery for the country's lenders.
BBVA and Barcelona-based Caixabank echoed some encouraging signs on Thursday from rival Santander, the euro zone's biggest bank, that its core lending business was starting to improve at the end of the year.
However their bad debts continued to rise as the end of Spain's recession in the third quarter of 2013 has yet to have an impact on cash-strapped businesses and consumers.
Spanish banks were hit hard by a property market crash and long economic downturn, which caused bad debts to shoot up as developers and households were unable to repay loans.
These pressures should start to ease, but with unemployment close to 26 percent - the second-highest level in the euro zone behind Greece - any turnaround in banks' fortunes will likely be slow.
Smaller Banco Popular on Friday reported a fall in net interest income (NII), its earnings from loans minus funding costs, in the fourth quarter compared to the third, in contrast to the rises posted by rivals.
Its bad loans as a percentage of credit rose to 14.3 percent at the end of December from 11.8 percent three months earlier.
BBVA and Caixabank's soured debt ratios were below a November sector average of 13.08 percent and both said non-performing loans increased at a slower pace in the fourth quarter from the third.
Spanish banks are hoping a pick-up in lending will start to buoy their underlying earnings after many leaned on bond trading gains to make up for weaknesses elsewhere last year.
Banks sold big chunks of their sovereign bond holdings in November and December to reduce exposures ahead of Europe-wide heath checks this year.
BBVA, which like rival Santander makes most of its profit in Latin America, expects a recovery in its Spanish home market where net profit halved to 583 million euros last year.
Chairman Francisco Gonzalez said he expected demand for credit to rise, as the economy picks up.
That view was echoed by Popular Chief Executive Francisco Gomez who also said a drop in the interest rates paid to savers on deposits should help boost net interest income. Deposit rates started to fall last year and the decline is expected to continue.
Shares in BBVA were down 0.8 percent to 8.77 euros per share at 1230 GMT, after rising earlier.
Caixbank shares were down 1.6 percent at 4.16 euros, while Popular's fell 4.0 percent to 4.96 euros, underperforming the European banking index.
STRONG LATIN AMERICA
BBVA's net income in Mexico, its biggest profit driver, rose 6.8 percent to 1.8 billion euros.
Many analysts say BBVA's heavier exposure to Mexico has given it an edge over arch-rival Santander, as growth in Brazil, Santander's biggest market, has stuttered.
Santander on Thursday said net profit in Mexico fell nearly 30 percent in 2013.
Several analysts warned, however, that BBVA may struggle to keep replicating the strong fourth-quarter earnings in South American countries such as Colombia, Venezuela and Argentina this year.
BBVA and Santander have both been trying to grow outside Latin America too, making pushes in the United States. BBVA's profits there fell nearly 12 percent to 390 million euros in 2013.
Caixabank, which has bought several smaller banks in Spain in recent years, said its 2013 profit more than doubled to 503 million euros.
BBVA's 2013 net profit rose by a third to 2.2 billion euros, slightly above analysts' forecasts.
It posted a fourth-quarter loss due to charges from selling a 5 percent stake in China's CITIC Bank Corp.
Popular reported a 2013 net profit of 325 million euros, up from a 2.46 billion euro loss the previous year. (Additional reporting by Jesus Aguado, Julien Toyer and Sonya Dowsett; Editing by Julien Toyer and Erica Billingham)