* Q3 profit 33.96 bln rupees vs estimate of 36.96 bln
* Higher provisions, slower loan growth weighs
* Shares slip 3.5 pct in Mumbai trade before recovering (Adds details, share movement)
MUMBAI, Feb 14 (Reuters) - State Bank of India, the country's biggest lender, posted a 4 percent rise in quarterly net profit, its smallest increase in six quarters, as higher provisions for bad loans and slower loan demand in a sluggish economy hurt growth.
Problem lending has risen in India as the country's worst economic slowdown in a decade clouds the outlook for banks including SBI, which accounts for a quarter of all loans and deposits in the country.
Net profit rose to 33.96 billion rupees ($631.40 million) for the quarter ended December, from 32.6 billion rupees a year earlier, the bank said on Thursday.
Analysts, on average, had expected a net profit of 36.96 billion rupees, according to Thomson Reuters I/B/E/S.
Net interest margin, a key gauge of profitability, stood at 3.7 percent at end-December, in line with estimates. Provisions rose to 26.7 billion rupees in the quarter, from 24.1 billion a year earlier.
The government-controlled bank, which has exposure to many of India's most beleaguered big borrowers including state electricity boards, Suzlon Energy, Kingfisher Airlines and Air India, said net non-performing assets rose to 2.59 percent of assets in the December quarter from 2.22 percent a year earlier.
SBI's gross bad loans, before recoveries and write-offs, stood at 5.3 percent of assets in the quarter, an increase of nearly a third from a year earlier at a time when analysts were expecting asset quality to improve.
The lender has been aggressive in identifying bad loans and making provisions since Chairman Pratip Chaudhuri took the reins in 2011. Its bad loan levels are above the industry average of around 3 percent.
SBI shares recovered ground after slipping as much as 3.5 percent after the results. At 1:20 p.m. (0750 GMT), the stock was down 0.6 percent. The stock is down 6 percent this year, underperforming the sector index that is down 1 percent in the same period. ($1 = 53.79 rupees) (Reporting by Swati Pandey, Writing by Prashant Mehra; Editing by Jeremy Laurence)