* Apple up 3 pct, leads tech after recent weakness
* Pace of "fiscal cliff" talks picks up, raising hopes
* S&P 500 regains losses since U.S. election
* Indexes up: S&P 1.0 pct, Dow 0.96 pct, Nasdaq 1.49 pct
By Gabriel Debenedetti
NEW YORK, Dec 11 (Reuters) - Technology shares led a 1 percent rise in major stock indexes on Tuesday, pushing the S&P 500 to its best levels since mid-October and erasing all of the post-election selloff.
The Nasdaq was lifted by a 3 percent gain in Apple Inc's stock to $545.37. The company's shares had dropped last week as investors took profits before a possible tax rise next year. Coming into Tuesday's trading, Apple shares had lost 25 percent from an all-time intraday high hit in September.
Other large tech stocks also rallied. Texas Instruments gained 3.5 percent to $30.88 after bumping up its profit target late Monday. That helped other chipmakers rally, with the PHLX Semiconductor index up 1.9 percent.
"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 rose 126.66 points, or 0.96 percent, at 13,296.54. The Standard & Poor's 500 Index was up 14.55 points, or 1.03 percent, at 1,433.10. The Nasdaq Composite Index gained 44.40 points, or 1.49 percent, at 3,031.37.
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.
"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.
But stocks have steadily marched higher on thin volume. The S&P 500 surpassed 1433.38 on Tuesday, retracing losses in the first seven sessions after President Barack Obama's re-election.
A positive report from Goldman Sachs Equity Research pushed up shares in some retailers. Luggage maker Tumi Holding Inc. was up 4.8 percent to $21.94 and Michael Kors Holding gained 4 percent to $51.76.
The U.S. Treasury is selling its remaining stake in insurer American International Group Inc. AIG's shares were up 4.1 percent at $34.74.
Unexpected improvement in data out of Europe set the positive tone early. In Germany, analyst and investor sentiment rose sharply in December, entering positive territory for the first time since May, a leading survey showed.
The Fed began a 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.