* S&P 500 recoups losses since U.S. election
* Apple up 3.1 pct, leads tech after recent weakness
* Hopes rise as pace of "fiscal cliff" talks accelerates
* Indexes up: S&P 0.93 pct, Dow 0.85 pct, Nasdaq 1.37 pct
By Gabriel Debenedetti
NEW YORK, Dec 11 (Reuters) - Rising shares in technology companies helped push major stock indexes up around 1 percent on Tuesday, as the S&P 500 reached its best levels since mid-October, recouping its post-election selloff.
A 3.1 percent gain in Apple Inc's stock lifted the Nasdaq, as the largest U.S. company by market value rebounded from a week in which investors took profits before a possible tax rise next year. Prior to Tuesday's trading, Apple shares had lost 25 percent from an all-time intraday high hit in September.
Other major tech stocks also rose. Texas Instruments gained 3.8 percent to $30.97 after bumping up its profit target late Monday. That helped other chipmakers rally, with the PHLX Semiconductor index up 2 percent. Microsoft rose 1.8 percent to $27.44.
"I see a lot of buying in tech, and that's taking the whole market up with it," said Tom Donino, co-head of trading at First New York Securities in New York.
The Dow Jones industrial average gained 112.57 points, or 0.85 percent, at 13,282.45. The Standard & Poor's 500 Index was up 13.23 points, or 0.93 percent, at 1,431.78. The Nasdaq Composite Index rose 40.95 points, or 1.37 percent, at 3,027.91.
Retailers like luggage maker Tumi Holding Inc and Michael Kors Holding gained on Tuesday after a positive report from Goldman Sachs Equity Research. Tumi was up 4.1 percent to $21.80, and Michael Kors gained 2.6 percent, reaching $51.08.
Traders voiced cautious optimism as the pace of negotiations over the "fiscal cliff" quickened. However, representatives from both parties cautioned that an agreement remains uncertain.
Republican House Speaker John Boehner called on President Barack Obama to propose a counter-offer on Tuesday.
"I guess in our own dysfunctional way, there is progress," said Frank Davis, director of sales and trading at LEK Securities in New York.
"Since conversations are occurring, it clarifies at least they are taking some action. My personal gut is they'll jostle this into the holiday week and try to do a last minute push."
Lawmakers worked toward a deal to avoid a series of automatic tax hikes and spending cuts that would hurt U.S. economic growth next year.
The lack of demonstrable progress has kept investors from making aggressive bets in recent weeks.
Still, stocks have steadily marched higher on thin volume. The S&P 500 hovered around 1433.38 on Tuesday, retracing losses incurred in the first seven sessions after Obama's re-election. Gains were broad, with more than two shares rising for every one falling on the New York Stock Exchange and winners outpacing losers on the Nasdaq Stock Exchange by nearly three-to-one.
The U.S. Treasury is selling its remaining stake in insurer American International Group Inc. AIG's shares were up 4.7 percent at $34.94.
The Fed began a two-day policy-setting meeting on Tuesday. The central bank is expected to announce a new round of Treasury bond purchases when the meeting ends on Wednesday to replace its "Operation Twist" stimulus which expires at the end of the year.