* BSE index up 0.31 pct, NSE index up 0.21 pct
* L&T falls for 3rd session over disappointing outlook
MUMBAI, Nov 3 (Reuters) - Indian shares swung between gains and losses on Tuesday, staying not far from their lowest levels in more than four weeks hit in the previous session, as concerns about earnings continued to weigh, although higher Asian shares supported sentiment.
Domestic shares have fallen for six consecutive sessions as of Monday, after some disappointment over earnings, including at economy bellwether Larsen & Toubro.
Foreign institutional investors (FIIs) have sold in three out of the previous six sessions, depriving markets of some momentum, after they had been heavy net buyers in October.
But sentiment was supported as regional markets have gained on hopes that U.S. interest rates are not likely to rise as quickly as previously thought, and on a growing sense of relief over China's growth numbers after recent official data.
"Last few days, the market was in a falling mode because FIIs were selling, the selling pressure has reduced and the market is stabilising (but) the fundamentals have not changed," said Deven Choksey, managing director at KR Choksey Securities.
The benchmark BSE index was trading 0.31 percent higher, rebounding after hitting its lowest intraday level since Oct 5 on Monday.
The broader NSE index was trading up 0.21 percent higher, recovering after hitting its lowest level since Oct. 1 on Monday.
Larsen & Toubro fell for a third consecutive session with disappointment over its earnings and outlook weighing on the stock.
Indian Oil Corp recovered some of its losses to trade 0.35 percent lower after the company reported a smaller quarterly loss than the previous year.
But some of the shares hit in the previous sessions rebounded on Tuesday. Infosys rose 1.1 percent after falling 1.2 percent in the previous three sessions.
Shares in Tech Mahindra were marginally down 0.15 percent while those of DLF were up 1.4 percent ahead of their quarterly results later in the day. (Reporting by Karen Rebelo in Mumbai; Editing by Anand Basu)