(Corrects to "Tuesday" from "Monday" in first paragraph)
* China cuts interest rate for second time in two months
* Oil prices rebound but still near 6-1/2-year lows
* Dollar touched session high
* Apple up 5.7 pct, BofA leads banks higher
* Indexes up: Dow 2.29 pct, S&P 2.45 pct, Nasdaq 3.19 pct
By Tanya Agrawal
Aug 25 (Reuters) - U.S. stocks posted their sharpest rally of the year on Tuesday, as investors sought out bargains a day after Wall Street's worst performance in four years on fears China's economy was slowing.
Markets also got a shot of good news with China's second interest rate cut in two months.
The Nasdaq composite index led the way with a 3.2 percent rise, boosted by Apple's 5.7 percent gain to $108.96. The stock slumped as much as 13 percent on Monday.
Analysts were cautious, however, and even with Tuesday's gains, the Dow and the S&P were on track for the their worst monthly losses since February 2009, while the Nasdaq was poised for its steepest monthly fall since November 2008.
"Today's rally can be attributed to value hunters who are slowly moving into the market as valuation levels now seem reasonable," said Terry Sandven, chief equity strategist at U.S. Bank Wealth Management in Minneapolis, while warning that a "wall of uncertainty" about global growth remains.
The move by China's central bank came after Chinese stocks slumped 8 percent on Tuesday following an 8.5 percent drop on Monday.
"What we need to see to calm investors is positive economic data points out of China and only when we see that will the rallies be sustainable," said Xavier Smith, investment director at Centre Asset Management.
"Right now, it's pretty meaningless," he said of the interest rate cut.
On Monday, the Dow Jones industrial average briefly slumped more than 1,000 points - its steepest intraday fall ever - and the S&P 500 recorded its worst day since 2011.
At 11:11 a.m. ET (1511 GMT) the Dow Jones industrial average was up 362.84 points, or 2.29 percent, at 16,234.19, the S&P 500 was up 46.47 points, or 2.45 percent, at 1,939.68 and the Nasdaq Composite was up 144.35 points, or 3.19 percent, at 4,670.60.
All 10 major S&P sectors were higher, with the technology index's 2.52 percent rise leading the advancers. U.S. banks rose, with Bank of America up 4.8 percent at $16.02.
Oil prices were up about 3 percent, bouncing back from heavy losses on Tuesday, but was still below $40 per barrel.
New U.S. single-family home sales rebounded in July and consumer confidence increased to a seven-month high in August, pointing to underlying strength in the economy that could still allow the Federal Reserve to raise interest rates this year.
Traders now see a 26 percent chance that the Fed would increase rates in September, up from 22 percent on Monday, according to overnight indexed swap rates.
The dollar, which fell to a 7-month low against a basket of currencies on Monday, was up more than 1 percent.
Disney was up 3.1 percent at $98.37.
Best Buy jumped 12.9 percent to $33.12 after the owner of the biggest U.S. electronics chain reported an unexpected increase in quarterly sales.
Advancing issues outnumbered decliners on the NYSE by 2,501 to 515. On the Nasdaq, 2,136 issues rose and 623 fell.
The S&P 500 index showed one new 52-week high and three new lows, while the Nasdaq recorded seven new highs and 48 new lows. (Reporting by Tanya Agrawal in Bengaluru; Editing by Savio D'Souza and Saumyadeb Chakrabarty)